They can use a conviction in the check case a couple of ways:
If found guilty the previous criminal record can be presented at the penalty phase. They seem to be getting as many aggravating factors as possible together.
It will also force some of these witnesses into sworn testimony. It sets the stage for perjury if any of these witnesses try to change their testimony in the murder case.
It will also prevent Baez from saying the check related events in the timeline need to be withheld from the murder trial as his client is facing charges related to those events. This will be very relevant in Amy's testimony.
In most jurisdictions you cannot enter a previous conviction as evidence in a current case as it creates bias in the jury. The state needs to prove the current case and when they do then the jury can be informed of the priors for the penalty phase. There have been many rape cases where the jury said they would have convicted if they knew about the priors but acquitted in a he said she said case for reasonable doubt.
JB will fight this going to trial first saying his client is fighting for her life in the other case and that this redirection of resources is unfair to his client. The state is usually pretty careful to make sure a DP defendant has had every opportunity to defend their life, so it should be interesting.
I was thinking about a question someone asked about prior bad acts, and how they could not be brought in as evidence in the murder trial. Guess I don't have to say, 
