It will work.
A TA-082 is just like any other PSP, only locations in the IdStorage have been switched around to prevent the 1.50 IPL from booting.
When you run the IdStorage changer, those locations are re-ordered in such a way that booting a 1.50 or any other firmware is possible. Therefore, the PSP is no longer a TA-082; the only remnants are some slightly different branding.
.'. Updating to 3.02 OE or any other firmware, even with a 1.50 kernel will succeed.
Trust me, so many people have done it. I did it on one of my old(er) PSP's before the TA-082 downgrader was released, following the discoveries of HarleyG, etc.
Your friend is safe updating.
