Will i lose games when i upgrade my HDD?

Hi, i am wanting to upgrade my PS3 harddrive but i'm worried i'll lose some downloadable games. The reason behind this is that most of my downloaded games were taken from a friends account and downloaded onto my PS3. I've found before that once you delete this persons account it will also delete the rights for you to play the game and it becomes unplayable. So if i backed up all of my ps3 data to an external HDD using the restore feature, copied all that to a new 250gig HDD, would it have all the accounts on and i could play all of the downloaded games including the ones i have shared.

Thanks

and P.S this person has used up his share 5 times right so i couldn't simply re-download the stuff.

If I'm not mistaken, before you upgrade your HDD, use the PS3 backup function and it will backup everything for you. Then install the new HDD. After that, you will need to run the restore function through the PS3. Once that's done, you can go back to PSN and redownload your games. You have to look in your download history for this.

This should work, but I am not 100% sure so please proceed at your own risk.