I would have a google on the subject.
You can pay for fairly inexpensive tests (just a couple of big drops of blood onto a test kit, and sent off through the post) which will give you a clear answer rather than speculating whether your mum is B12 deficient. That will also let you know how deficient she is, which will likely help you in choosing the appropriate B12 supplement.
B12 supplements vary a great deal, from dose, to tablet or liquid, and B12 comes in several different forms which in turn are variously absorbable. There is a huge difference in price too.
There is lots of info out there, and your choice is going to depend on whether your mother prefers tablets or liquid, and what your budget is.
My personal advice would be to avoid the cheap generic stuff and go for decent quality, provided you are not breaking the bank.
.
When I was severely deficient in B12 a couple of years ago, I was recommended a 30ml dropper bottle that cost £60
I paid for it (in horror) and it worked like a charm.
But now I am on a maintenance dose I shop around, buy a lower dose, a different brand, and am confident that I don't need to spend big bucks like that again, unless I get very deficient again, which is very unlikely, now that I am educated on the subject.