If MIL hasn't personally claimed credit for the gift, I might not even send a thank-you yet. What if it wasn't actually her? Is your relationship with SIL good enough that you believe her? Not questioning SIL on her ethics. Just would hate to open a can of worms with MIL if she didn't even send it in the first place.
If my MIL says something (she's at the top of the bat-s*^t crazy list) its always taken with a grain of salt. If SIL or BIL tell us something she said we can almost be sure they got a half truth.
I would also agree with PP who have said to cut contact on FB. Step-MIL should too. Doesn't sound like anything good can come from communicating with her at this point.