Your priority date didn't become current yesterday. It will become current on June 1st. The dates in visa bulletin don't take effect on the day the bulletin is published; they take effect on the 1st day of the named month (in this case June).
She can go ahead and travel as long as she has a valid Advance Parole when exiting and reentering the US. If her GC is approved when she's abroad, she can still use the unexpired AP to reenter the US. After showing AP at the POE, they will see her GC approval in the system and register her admission as a permanent resident.
However, if her last fingerprinting was more than 15 months ago, there is the possibility of having to attend another appointment before they will approve her GC. So she should be prepared to return to the US on short notice to attend the appointment. Rescheduling the FP would be a bad idea because retrogression could kick in before she gets another appointment.