The bureau shall promptly assign each claim and application, and notify the claimant or applicant of the identity and address of the assignee of the claim or application. Claims and applications shall be assigned so as to minimize inconvenience to claimants and applicants. The assignee, thereafter, has rights and obligations as if it had issued motor vehicle mandatory public liability and property damage policies complying with this article applicable to the accidental harm or other damage, or, in the case of financial inability of a motor vehicle insurer or self-insurer to perform its obligations, as if the assignee had written the applicable motor vehicle insurance policy, undertaken the self-insurance, or lawfully obligated itself to pay motor vehicle insurance benefits.