If Firefox is maximized then make the window smaller and drag that window over to the correct monitor and close Firefox to save that setting.
After restarting you can maximize again.

Window sizes and positions are stored in localstore.rdf in the Profile Folder.

• http://kb.mozillazine.org/Corrupt_localstore.rdf

This is not helpful. In my case I have 6 monitors on an eyefinity graphics card. This suggestion may cause the window to open on the correct monitor once, but as soon as you close it on a different monitor it will default to that monitor. This is quite troublesome as 4 of my monitors are in different rooms of the house (every monitor is 1080 so i can mirror it with my main monitor and stream media to any tv in the house). :( Even the monitor in the same room isnt always on. I have to hold the windows key and arrow around until it shows up on the right screen and sometimes it takes forever like a puzzle. Stupid firefox. Its easy to set internet explorer to default to one monitor. :( sadly ie is my only solution atm. the worst was the time firefox opened a private message on my kitchen/cooking screen! ughhhh. everyone in the household read it.