The title basically says (or asks) it all. I downloaded an ebook to my Sony account, but I gave my reader as a gift to someone else (so it's on their account). Obviously, since their reader is authorized with their account (and not the one that downloaded the book), it can't read the book.

Is there any way to transfer the book over to the other account so that it is readable on their device (without having to re-buy it)?

I'm going to contact Sony about this as well and see if they can help.

Give them access to your account. That's the only way. Sony ebooks cannot be transferred.

You will have to allow the person who you gave the reader to to authorize the reader to your account. Then that eBook can be transferred and read. Once read, have that person authorize the reader to his/her account again so any eBooks purchased on his/her account can then be read. But the eBook you purchased won't be readable.