Assignment, i.e. a change of domain subscriber, and transfer are unrelated.
You can transfer the domain if you have the authinfo code and access to the mailbox in the domain registrant’s details to be able to confirm the process.
Transferring the domain, i.e. changing the company where it is registered and paid, will not change the registrant’s data.
So, for example, having authinfo and access to the mailbox, you can transfer the domain, e.g. from the service provider where the domain is currently registered to mybox.com and then order the assignment procedure, i.e. the change of the legal domain registrant, according to the guide available HERE.
Remember
If you are interested in moving your domain to new registrar, please contact our support and we will prepare an offer for you.