EDIT: I'm leaving the below, but I may be a bit confused between Favorites and "Google Bookmarks"...I assumed it was the same thing you were referring to, but maybe not.
I don't know if this will help, but this is what I do: I use XMarks, which basically will sync your bookmarks across all your browsers. I use Firefox, Chrome and IE depending on the task at hand, so no matter which browser I use, all the bookmarks are the same. So I bookmark something in Chrome, it shows up in IE and Firefox (and vice versa).
Here's where it gets cool though...XMarks is free to sync PC browsers, but they charge for mobile syncing. But with Chrome it doesn't matter, since Chrome syncs to itself.
So say I'm on the PC and bookmark something in IE. Well, it syncs to Firefox and Chrome, and since it's no in Chrome (on the PC) it syncs to Chrome (on my phone and iPad).
It works out really well for myself. What you would need to do in your circumstance is to leave Chrome open on your computer at home (so if you favorite something in Firefox, it syncs over to Chrome, and then to your phone).
It works well for me, but I can foresee a couple issues with your situation....since if you have personal bookmarks at home that you don't want on your work PC (with Firefox) then that's going to be an issue. Also, if you don't use Chrome at work, you'd have to leave it open on your home PC (so when you bookmark something in Firefox, it syncs to XMarks, then to your home PC/Chrome, and finally to your phone)