A Romero motion derives from a 1996 case called People v. Romero. In Romero the California Supreme Court said that in sentencing, a judge can ignore a defendant's prior criminal record. A Romero motion is sometimes called a "motion to strike a strike."
A Romero motion is hard to win. However, if there is some light that it could prevail then it should normally be made. Sometimes there can be reasons a defense attorney may suggest not to make such a motion. A motion in California is normally heard within about 30 days after it has been filed. The court can rule on the motion at the time of hearing or take it under advisement and rule later.
Romero motions are made/filed after conviction, but prior to, or during, the actual time of sentencing.
The age of the prior strike as well as the type of conduct (past and present) are usually important factors the court will weigh in making its decision.
32 month offer seems like low term for the new charge (16 months) doubled because of the prior strike. If there is a stipulated plea agreement with the DA, a Romero motion would be fruitless.
A motion to strike a strike will only be granted in the interests of justice as determined by a judge. It's a safety valve that enables those who deserve it a chance to avoid the effects of CA's 3 strikes law. It is never guaranteed that such a motion will be granted; however if it were it would reduce the sentence on the new offense. I would add that I have seen some very sad cases were one would expect the motion to be granted and it was denied. It depends on your facts as perceived by your judge.
A Romero motion CAN be filed and granted prior to entering a guilty plea, despite the information another attorney posted. It makes no sense to plead guilty without addressing the Romero issues with the judge first to get the benefit of the bargain.
Those are tough facts for your fiance because his strike and prison release are so recent. It is possible if there are strong equities in your fiance's favor but the recentness of the strike is his biggest obstacle.
If the court grants the Romero motion, he will likely strike the strike that day and the same day your fiance will enter his plea.