Users must have admin or owner rights within the receiving organization before they can transfer a repository that they individually own. If the user does not already have this level of access, a temporary admin team can be created with only the user. The user sending the repository is the only one who can perform the transfer.
Just as when transferring a repository between two organizations, when a repository is transferred from a user to an organization, the Owners team is the only group with read/write access to the repository, but they can choose to add other teams for further access. See "Permission Levels in Organizations" for more information.