I can feel one implant move more than the other one, is this normal?

Yes, some differential breast implant movement is quite commonly experienced.  If the movement is excessive, where the breast implant moves too much, this is a problem called breast implant displacement or malposition.  In my practice, I ask my patients to wear a supportive bra for many months after breast augmentation surgery, even when in bed.  Best wishes.

Hello
dear, thanks for your question and provided information as well…
I have to say that you are still early on healing process, it is too soon to
determine how your results are going to be, per now, they look very nice and
beautiful, you can have one bigger than the other, feel swollen and also have
bruises and open wounds, it is normal and that can happen for the first 3 to 4
months until your implants have settle in. I recommend you to wait and keep
using your post surgical bra, that will help you with the shape and support!!

First, you did not state when you and surgery, In general, each breast will respond differently and certainly one may move around more in the pocket.