Assuming you are using a Transformer for import, blend-shapes cannot be imported along.
CC has it's own extensive face expression morphs and visimes which applied after the import.
You may import some desired expressions later on if you wish, but only one at a time:
Dial the expression in DAZ, export, import via transformer with Basic.
Export as OBJ > Nude character in Bind pose.
Load originally imported character, go to Edit Expressions, click New Slider and import the OBJ with custom expression.
Note: Avoid importing DAZ expressions which have distinct head/neck movements. Those will not import properly.