I've been using CC3 for several months to try to learn how to make a 3D character from a photo using Headshot.
Headshot somehow fails to create the exact outline of the face or any part thereof from the photo in the Auto or Pro mode.
I had to use the Active Image Matching Tools to manually adjust the detailed contours of the eyes, nose, lips, ears, and face of the character so that all those elements have the exact same contours as the original photo. I usually adjusted the opacity of the original photo while adjusting the character.
This was not easy. Especially getting the nose and eye shapes right was really painstaking.

After I finally reached the level of exactness I wanted, I saved the character and sent the character to iClone for animation.
But somehow the character sent to iClone looked a bit different from the original photo. I thought it was because it looked darker due to the different lighting settings in iClone and CC. Then I noticed that the iClone character looked a bit fatter than the original photo in the same lighting setting.

I was searching for the reason and I think I finally found it. When I bring up the saved character by applying the saved character to the CC default character in CC, it does look fatter than the original photo (even though I did match it to the original photo before saving it). What's funny is, when I go to the Headshot tab and turn on the Active Image Matching Tools to examine exactly where the saved character doesn't match the original photo, the character does match the original photo just like when I saved it, the reason being somehow at the moment I turn on the Active Image Matching Tools the character suddenly becomes leaner to match the original photo. Now even after I turn off the Active Image Matching Tools, the character stays leaner.

But when I send the completed character to iClone right after turning on the Active Image Matching Tools and confirming it matches the original photo, the iClone character turns out to be fatter than the original photo. What is happening??

Does this mean I cannot animate a character that exactly matches the photo using the Active Image Matching Tools in Headshot?

I think you may need to adjust the lens a bit. Basically your perspective between the 3D model in the scene, and the photo are mismatched. See "D" on this page of the manual.
https://manual.reallusion.com/Headshot_Plugin/ENU/Headshot_Plugin_for_CC/1.0/ID_SA_IMT_Pro.html
Ajust the perspective so the edges of the head of the 3D character and photo pretty much line up.

I don't know what the perspective is, but I don't understand how to adjust the lens. 
Currently, the 3d model is morphed enough to fit the photo. So the 3d model doesn't need any further adjusting. That is, the edges of the 3d model and the photo all line up as is.
How do I go about further adjusting the perspective from here?

In addition to what Rampa says, it's also possible the lens in iClone itself isn't matched up.  

Folks look different depending on the lens used by the camera.  iClone has a "digital" equivalent.    If you shoot someone with a telephoto (say a 200mm lens) you will see their features all flatten out (they will look "fatter") but if you shoot someone with a wide-angle lens the features get exaggerated to each other (although the head itself will look thinner.  Ideally a good portrait lens is around 80mm.

This has nothing to do with the relative size of the head, as you can move (dolly) the camera closer or farther to get the same width.  So try it yourself in iClone -- make an 200mm lens and then dolly the camera until the head fills the frame.  Render that image.  Now make a 35mm lens and move the camera closer (dolly it, don't adjust the length of the lens) and compare the two images and you'll see how the face looks very different depending on the lens.

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Alienware Aurora R12, Win 10, i9-119000KF, 3.5GHz CPU, 128GB RAM, RTX 3090 (24GB), Samsung 960 Pro 4TB M-2 SSD, TB+ Disk space
Mike "ex-genius" Kelley

Thanks for the info. I think I see where you're coming from.
The manual linked by Rampa says that the lens value in iClone indicates the focal length of the camera which took the photo. 
The photo file's properties (on Windows 10) show two values:
(1) Focal length = 3mm
(2) 35mm focal length = 32
Since the iClone lens value is between 10 and 70, I think that (2) has to be the value, and that the lens value in iClone should be set at 32. Am I right?
If so, should I set it at 32 and then morph the head again to match the photo?

I think you need to experiment.  32mm for a (35mm) camera is a pretty wide angle lens, and one that is NOT flattering to the subject at all.  But it depends on the effect you want.  Do as I said and try a few different views, dollying the camera in or out to get the size right, and see what you like.  

As to what's "accurate" -- a 50mm lens is considered to be the same vision as you eye.  So if you are trying to create a character or make it look as you truly see them, that's the lens you need to shoot for.  It's complicated because the lens that took the original image (the one you are using to match up in CC3) may be a lot wider or narrower than this.  So it's all down to what looks good to you.

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Alienware Aurora R12, Win 10, i9-119000KF, 3.5GHz CPU, 128GB RAM, RTX 3090 (24GB), Samsung 960 Pro 4TB M-2 SSD, TB+ Disk space
Mike "ex-genius" Kelley

I don't want any particular "effect". All I want is to make the 3d character look as close to the real person of the photo as possible.
In that case, should I set the Headshot lens value to 32, remorph the character to match the photo, and send it to iClone, where I should set the focal length of the iClone camera at 50mm?
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I just did it. And it doesn't seem to work. 
Now, let's just not talk about the lens for a moment.
The issue I originally have is why the character I make using extensive morph adjustments in CC cannot be imported into iClone as an exact duplicate.

Remember that iClone isn't set the same way as CC3 is -- Rampa can elaborate (I don't have the time right now).  NO character imported from CC3 into iClone will look the same unless and until you apply some very specific adjustments to the scene.

Let Rampa elucidate (and, again, remember the lens used to take your reference photo plays a BIG part in all of this).

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Alienware Aurora R12, Win 10, i9-119000KF, 3.5GHz CPU, 128GB RAM, RTX 3090 (24GB), Samsung 960 Pro 4TB M-2 SSD, TB+ Disk space
Mike "ex-genius" Kelley

As Kelley already mentions, you would also have to know the lens settings of the original portrait photo and the angle with respect to the face. Ideally, the original photo would be straight on, but often it is not. For example, I often find that the ears are too high or too low. 

The best Headshot can do is assume a more or less normal face. Headshot photo matching changes the lens setting so that the contour can be lined up with the model, but the only goes so far.

What I mean is that you may try to adjust your model to a face with a somewhat distorted perspective. To get an exact replication under these circumstances would be very hard.

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Is this photo one you can share? We can probably make the description using your own photo to demonstrate.