Can iTunes songs be transferred from one account to another account?
No, unfortunately, you can not change 'ownership' of the files to another account. You would have the same issue with a married couple that bought all the music on one account, but then got divorced. This happened with my dad and his ex-wife's account, and we contacted Apple to make sure.

The most 'legal' route would be to possibly convert this current account into his new account. As in, change the contact, billing, and email address to use his info. This way, his account just moves with him. If you ever wanted to make an account, you could create a new one.

The closest thing you could possibly do otherwise is when he has his second account set up, turn on Home Sharing on both machines. He could then add this music to his new library, and your account could authorize it. 

Another option would be to possibly use iTunes Match. He could copy all of the files he purchased into his library, and turn on iTunes Match. Then delete those files locally, and re-download from iTunes in the Cloud. This would remove DRM on some files, so he could play them, and have them in his library. (This is the path my dad chose).

The legality of either of the last two methods though is questionable, since that's not really the design of the service. Although, this may be more of the 'right' thing to do than illegally download them. I am not a lawyer, so what I say in regards to that is only in observation or feeling, not official.

In the end, with DRM'd files, and many Terms of Use of digital files, the purchaser is the only one who owns the 'rights' to the files. While he may have purchased them on an account you owned, you are actually the owner, etc. iTunes does not let you transfer this ownership, but they do provide services like the two above to help families.