Hi Frank,
My understanding is the passed exam is valid for 1 year in terms of counting towards certification. There is no "renew" for an exam, only for a certification.
Assuming the above is correct, if you can pass one of the prerequisite exams before September 22nd, you will earn two certifications. Once you have the certifications, then you will be able to renew them (for free) before they expire (1 year from date earned), unless a certification is retired.
If you wait until after September 22nd to pass one of the prerequisite exams, then I don't believe you will earn Microsoft 365 Certified: Administrator Expert certification since it will have been over a year. This is based on someone else that posted.
If you like, you may verify the information by asking a question on the Microsoft Credentials forum:
https://trainingsupport.microsoft.com/en-us/newthread?threadtype=Questions&forum=mcp
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP