Promotion soon after transferring to a different agency?

Can I negotiate a promotion before accepting the final job offer (FJO)?

Here’s the context: Currently a fed working as GS-11 (52-week mark in Nov 05 as GS-11), and have recently been extended an offer at another agency - different series than my current position (0201 vs 1801).

The thing is, I have already been put in for promotion for GS-12 around the Nov 05 date at my current agency. I know this because my current supervisor sent me the email confirming this. Can I use this info to negotiate the same with the gaining agency on my promotion - that even if I start as GS-11 now, they consider me for GS-12 come November? Both positions go to GS-12. How should I approach this?