Green card with new employer Part 2

I have received an offer letter from a new employer.
I am on h1b visa with approved i140. My pd is 2015.
I tried to negotiate green card with new employer to start earlier like in 6 months. As I expect my date to become current in the next few months and new perm takes 6 months to a year.
They are willing to give that in email but not on the offer letter.

Is this sufficient what should I get so it’s legally binding. Any advice is appreciated.

My current employer has started layoffs. I am trying to proactively move before I get the boot

Email can be treated as a formal e-document. I think most employers follow through on such commitments.