H1B employer asking resignation letter 5 months in advance

[ForSure]

Hi,

I work for a non-profit organization on H1B-nonprofit and my first H1B term ends in April. My current contract ends in June and the HR policy is to promote me after June in order to continue working. My HR advised my boss to promote me from April for them to process the H1B extension just once and get down with it. But my boss says he doesn't have a position to promote me in April or after June and is willing to support for H1B extension until June. 

My HR is now asking for a resignation letter dated the end of June to process the H1B extension paperwork. Should I do this?  what are the consequences, if I plan to resign before June? Why is this required when my contract clearly says the date the contract ends shouldn't it be automatic termination when the contract ends?

Please advice.

FS