Can I contact my old business partner’s current employer to tell them she has been currently charged with 3 class B felonies for theft and to be careful?

Technically, truth is a defense to a defamation suit, so if the information is true, you can tell anyone, including her current employer about the pending charges.  Be care at this point to make it clear that the charges are pending. 

Even though you can call the current employer, be mindful that you may be causing more problems for yourself than the phone call is worth.  First, if the current employer misunderstands what you said-- such that the way they received the information is not correct, your old business partner may decide to file a suit against you for defamation.  You could defend the suit, but only after the headache and financial stress of hiring an attorney.  If the current employer decides to terminate her and she had an employment contract, then she could also file a suit for interference in the contractual relationship.

It sounds like you want to be helpful to the new employer, but it really is up to the employer to conduct a proper background check to avoid issues.  There is a saying that "no good deed goes unpunished."  Trying to help this new employer could create serious liability issues for you.  So really think hard about how and if you are going to tell the new employer about her history.