Can I use an AT&T iphone on SPRINT after unlock?

I have an AT&T factory unlocked iphone 3GS and I was wondering if there could be any way to use it on Sprint as I'm planning to give it to my aunt.

No, and for two reasons:

1.) The iPhone 3GS is a GSM only phone (so is the original iPhone, the iPhone 3G, and the AT&T iPhone 4). Sprint is a CDMA carrier and as such the phone is incompatible with the network.

2.) Sprint does not currently allow outside phones in it's system. You need to provide the ESN of the phone to Sprint to activate, and even if the phone was CDMA, if, it isn't provisioned for Sprint from the factory, it will not work with Sprint.

No.

All AT&T devices use GSM.

Sprint uses CDMA.

There's no way to make a GSM device work on CDMA networks.