If you friend used a promo code when he purchased the hosting plan, the plan is considered as a promotional plan. According to DH, users are not able to transfer domains between promotional plans.
If the plans are not promotional plans, you can simply file a ticket to DH support. They will transfer the domain after your new plan is activated.
If you want to continue with the domain name, you may want to try to ask your friend to grant some access on the domain to your new plan via DH panel --> Billing --> Accounts Privileges
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