FP2 processors are soldered to the motherboard, so no.
If you used CPU-Z to determine that you have A8-4500M in socket FP2, then note that CPU-Z mis-identifies the socket. The A8-4500M APU is PGA socket FS1r2, and it is replaceable. Maybe try HWiNFO or AMD Overdrive to crosscheck the APU identity and socket type.
HP does not list any faster APUs that are compatible, so I can't say 100% whether the newer A10-5750M will be compatible. However, I was able to accomplish the same upgrade on a ProBook 645 no problem. You will probably want to ensure BIOS is up to date before the swap.