Originally Posted by web3k
All TLD domain transfers to my knowledge require you to pay an additional years registration charge (.com, .net, .org etc).
TLDs require either re-registration, or renewal on transfer
TLDs vary by country, with about equal numbers between
* not allowing transfers
* not charging for transfers
* renewing on transfer
* starting as a new registration on transfer
Regarding the OPs question - whilst it's not clear that they understand the difference between *files* for hosting and the *domain* the simplest answer is
Yes, you can transfer it (subject to various dates/rules/regulations) - whether that's the site you're transferring (which will "cost" you in time to do it) or the domain you're transferring (which in the _main_ will cost you to do so).
If you choose to charge your client or offer it free, that's all down to your own business model - it wont alter whether there is a cost to you to offer it.