https://www.epo.org/en/service-support/faq/law-practice/unitary-patent/requesting-unitary-patent/how-can-i-request

How can I request a transfer of rights for a Unitary Patent?

To request and register a transfer of rights for a Unitary Patent, you must provide a written request, evidence of the transfer and pay a fee as per Rule 20(2)(b) UPR and Rule 22 EPC.

If a transfer of rights is allowed for a European patent (Rule 85 EPC), it can also be simultaneously requested for the Unitary Patent, using Forms 5050 and 5055. No separate request and no payment of additional fees are required. Requests submitted via MyEPO Portfolio are free.

The transfer will be registered in the Register for unitary patent protection and, if Rule 85 EPC applies, in the European Patent Register.