First off, I'll say that it probably won't have good running stability, but you should at least try to use the trem. But don't be surprised when after fixing it countless times that it'll need to be replaced. Here are a few recommendations for some replacements.
Even though I personally have no experience with it, I'd recommend a Gotoh Floyd Rose. It's about $80 cheaper than an Original Floyd Rose. Gotoh also makes the Edge tremolos for Ibanez, which are regarded as the best tremolos you can find on a guitar, so you know they're experienced in manufacturing these types of trem systems. Naturally, many people here and on the Ultimate Guitar forums praise the Gotoh trem. Again, I have no anecdotal experience with these units but I'm saying what I've read from other guitarists.
A Floyd I've had experience with is the Special Floyd Rose. It's $55 on Ebay, and it's been kind of a pain in the ass. Some saddle screws have stripped, the fine tuners are stiff, the arm collar has cracked, the string blocks are having trouble holding the e and B string, and the hex on the nut is starting to strip. For its price, it's great. It functions just as intended. But I have this gut feeling that I'm going to have to replace it sooner or later.
Of course, you'll want to check dimensions for compatibility before buying.
My final words of advice is that Floyd Rose trems are very finicky, especially for a beginner to guitar setup. So do your research, and be careful. Don't wanna be breaking your replacement! One tip I can give is that if the strings go out of tune even when it's setup perfectly, try putting Vaseline on the knife edges. It helped me.
Sorry for the wall of text.
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