What kind of physical therapy movement would help mom gain strength in her hand after suffering from a stroke?

Great suggestions already given. I would like to add that you can probably find videos on Youtube for this. I am presently learning some Yoga hand and arm exercises that I have looked up on Youtube. I plan to do them with my mother in the nursing home to keep her strength up.

There are plastic resistance devices with rubber bands that physical therapists use. Additional resistance is added by increasing the quantity or decreasing the size of the rubber bands. Inexpensive and they work well.

After total hip replacement, I had PT sessions at local center and noticed a section where patients where doing PT exercises specific to hand therapy. So there is PT available. Consult with her doctor and ask for prescription for her to start PT.

As a kind of first response answer in case the stroke was recent or severe: you immediately need to keep your mother's hand from curling up. Use a face flannel, muslin square or even a clean duster (any clean, dry, lint-free, absorbent fabric); roll it into a sausage shape; and tuck it into her palm to keep her hand in a comfortable, loosely open position. Change the "roll" frequently (morning and night, more often if it gets sweaty faster). Wash, rinse and dry her hand gently but *very* thoroughly. You'd be surprised how much one little hand can sweat, and if it is curling up yeast infections will love it.

If your mother's stroke was not so severe, an OT as Barb suggests or a physical therapist will teach you techniques for regaining the use of her affected hand. I'd expect this to be routine follow-up care - hasn't it been offered?

If she is not being seen for it then may be a small (hand size) soft, sponge ball, for her to squeeze on.

Is she being seen by an occupational therapist?

Is she currently in rehab for the stroke?  

Google "thera-putty" which is a graded flexible putty that OT's use to help stroke patients exercise hands.