We cannot transfer account ownership or change the login method attached to an account. However, you can transfer the project to your client's own Railway account. Have your client create their own Railway account and subscribe to a plan, then invite them as a member of the project under Project Settings > Members. Once they've joined, click the three dots next to their name and select "Transfer Ownership." They will receive an email to confirm the transfer within 24 hours. More details are in our project transfer docs.

This won't work as this a hobby account not pro.

Project transfers work on Hobby plans too, not just Pro. Your client just needs to create their own Railway account and subscribe to the Hobby plan ($5/mo). Once they do, you can invite them to the project under Project Settings > Members, then transfer ownership to them.

Will the credit on the current account be transferred or will they be paying twice?

Credits are tied to the account, not the project, so they won't transfer.