Good job. I'm sure it will work just fine for her.
I worked violent crime on Indian reservations in the wild west for 17 of my 25 years in the FBI. I worked many, many shootings (both fatal and non-fatal) and the predominant caliber was the lowly .22 LR (because everybody had one.)
I didn't have a single shooting where a person continued their aggressive behavior after being shot (or shot at) with a .22 caliber weapon. Not one.
I have come to believe that hardware (gun type, caliber, ammo selection) is the least important aspect of self defense.
PS - when my geezerly wrists and hands finally succumb to years of .45 caliber abuse, I have a very nice Beretta Model 87 .22 standing by to see me through my golden years.
