Suspending a thief will have an effect, but since she's out of play for a week the case can't progress until she gets back. (Which is why the card is prominently labeled with when the character is expected to return, to try and give an indication of when something will happen.)
On the best friends:
It felt like either C was lying and she actually was intentionally stealing A from B and I could expose this somehow, or alternatively B was just being oversensitive and there was some way to force her to confront the fact that she could still very well be friends with A, if she just so chose. But I never figured out how I was supposed to do either.
If you feel that the new friend is lying, harassing her
will move the case along, and I think most people currently solve it this way. It's not the only answer though.
Figuring out what's going on with the 'oversensitive' girl is possibly a little too tricky. Currently the only way to open up the option to punish her is to get evidence from her roommate. Possibly she should also leak some clues on a successful persuade check... I'll think about that.