A couple of miscellaneous thoughts:
1. If she received the ~$700 as a direct deposit, she could look at the description. If it says "Treasury 310" or something like that, it's the stimulus payment. If not, it's probably her SS.
2. SS deposits have been a day or three early lately. I've seen multiple people report this. The timing being early might be what has confused your MIL.
3. About two weeks after her stimulus payment is sent, she'll get a separate piece of paper in the mail from the federal government informing her of the amount of her stimulus payment. She can use that information to figure out how much her stimulus payment was.
4. +1 to filing and getting the rest of it on her 2020 taxes and the "Where's my Payment?" tool.
And yes, based on the information you gave, assuming she's single and nobody claimed her as a dependent, she should qualify for the full $1200.