Just got an offer, how to contact other interview processes

I got FT offer today on the phone (let's call it Firm 1) and was wondering how to reach to another interview process (Firm 2) where I had last rounds last week. I'm impartial about both, and don't know how much comp would be in Firm 2 (may be more).
How would you go about reaching Firm 2? I don't want to say I got an offer from another firm but would highly prefer Firm 1 because that is not the case. I just want to have both offers on paper to be able to make a decision (and know if Firm 2 would hire me).

 

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