Officially bought Games from PS Store

Hello lovely People
I have a PS3 Slim that is NOT jailbroken and I have Games on there that I officially bought.
I will get a Jailbroken PS3 with REBUG 4.84 DEX in the Mail.
Is it possible I can redownload my PS1 and PS3 Games that I officially bought from the Store or can I save them to USB somehow and transfer them over to the new Jailbroken PS3?
Any help would be much appreciated.