Easy memory question for xmas gift

i'm buying my mother computer memory for christmas because her computer is so damn slow. I want to make sure her christmas gift actually works so i have a quick easy question.

The memory current in her computer says Toshiba PC100-22-620

also 16mx64

The memory i'm looking to buy her says

Toshiba
THMY36E11B-80
PC100-222-620
32Mx72 SDRAM

the only difference is 32Mx72 vs 16mx64. Will this be compadible with her system? Basically will it fit just fine in the motherboard slot ?
Do i need to buy her only a 16mx62? (i'm fairly sure the answer is no). The computer guy said he thought her computer (he has NEVER seen it) will not support anything bigger than a 64 memory chip. I think he's full of it having done pc repairs YEARS ago. Hopefully i can give her a big boost in memory and buy her this memory stick right away. ANY advice would be super helpful. Thanks!!

The memory you're looking at is 72 bits wide instead of 64, meaning it is ECC memory. It's not really the best idea to mix standard and ECC memory sticks together, although it can work... Also, not many chipsets (particularly lower-end ones) support ECC at all.

Really you should find out what chipset her machine is using, and go from there..

There is some info on what the 16mx64 means and whatnot here but it'll still be easier to see what chipset it uses because from that you'll know what the maximum size of stick is that it can fully utilise.