I've seen these payroll mistakes all the time, especially here in the "DMV" (DC, MD, VA).  If I know about it I'm pretty diligent about advising clients to notify their HR/Payroll department as soon as they move.

But more often than not, I find out about it after the fact.  Have them pull paystubs around the time of the move.  You should be able to figure out MD source based on YTD before the move and maybe have to prorate wages if they moved in the middle of a pay period.  Everything after the move will be WV source because of the reciprocity agreement between MD and WV.  Around here folks are taxed in their resident state rather than the state where they work.  MD has reciprocity agreements with DC, PA, VA, and WV.

You'll need to convince ProSeries by putting the appropriate amounts in the state section of the W-2 (so basically ignore what's entered there and put the correct wages).  Then you'll fill out the PY section of the Info Wks (scroll way down and put the dates for each state).  That will let you open up a PY allocation Wks (linked to from that area).  If you're lucky, the wage data pulled correctly from the W-2.  When you finish your federal 1040, fill out the rest of that PY Wks to enter interest, dividends, etc. in their appropriate state.  After that you can open either state, shouldn't matter which one you do first.

Hope this helps, it's kind of a cumbersome process but I don't see a better way around it.  I explain to folks on intake that it usually takes 3x as long to do the part-year returns.  Around here the state returns practically prepare themselves once you've done the federal.  But with PY you have to do the federal and then you have to do each state basically from scratch since you have to tell the software how to source each piece of income.

Rick