According to various posts over at the official PlayStation forums, PSP firmware 3.80 and PS3 firmware 2.10 have silently added new functionality to allow users to play PS Store-bought PSOne games and original PSOne game discs on the PSP through Remote Play.
PSOne games via Remote Play also works with firmware 3.71. So as long as your PS3 is updated to 2.10, you can take advantage of this functionality even on a homebrew capable PSP.
To quote: Users have been reporting that Remote Play has been secretly updated in the last firmware revision. With PS3 2.10, PS3 owners that have a Remote Play-ready system will be able to play any PS1 game on their handheld. Yes, that includes both games downloaded from the Store and PS1 game discs. We've personally tried Wild Arms (the downloadable version) and confirmed that it will play via Remote Play. Our tipster tried playing Metal Gear Solid (on disc) and also found that it works. Happy news!
We find ourselves using Remote Play more and more with the inclusion of DivX and WMV playback. Now, PS1 support will increase our time spent with this feature.
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