Keystroke Logger ??

Suse 11.4_64

My wife's Facebook account keeps getting hacked. She changes her password and within 24-48 hours, someone hacks it again. The hacker actually changes the password, which he cannot do unless he has the prior password. These are not passwords that can be guessed.

I'm not very knowledgeable about hacking. But it seems that the only explanations are a security problem with Facebook's password list or a keystroke logger. If its a keystroke logger, where would I look in the file system for some evidence?

My wife has her own computer.
Its just her and I in the home, no kids.
She uses Firefox's password wallet.

Thanks in advance for your help.
I'm not a regular here, but I always get answers in this group when I need them.