Metformin is used in the treatment of PCOS (which is driven by insulin resistance) and hair loss is one of the horrible PCOS symptoms. So I doubt the metformin is causing the hair loss since if it were there'd be a major outcry from women with PCOS, but it can cause depletion of Vitamin B12 (NancyLC- not sure if it's both but definitely B12).

Not sure how old your mum is but she might even have PCOS.