I can't give a definite answer, but I'll give some input to try help.
There are some good answers on related scenarios here:
https://islamqa.info/en/answers/6560...-heavy-sleeper
Fajr is the most important of the 5 salah. If one misses it, one is required to offer it as soon as one remembers (and I would sincerely repent each time for reading it late). One should try not make it a habit to miss it, and try the best to make changes that enable you to consistently read Fajr on time. Can she find a way to sleep earlier?
May Allah guide your mom to make the best decision, and make it easy for her to read Fajr on time. May He remove her health issues and give her the health and strength to read salah standing without difficulty.