Is there a way to share my template with another JotForm user?

My colleague didn't know how to use it, so I set up a registration form for them but I want to send him the template so he can integrate his payment info on his own. 

Yes, you may share the link to the form, then the form can be cloned by following this guide: How-to-Clone-an-Existing-Form-from-a-URL

Payment integration will need to be set up in the cloned form in order to get it working. 

Hope this helps.