Review: Microsoft MapPoint
No. Maps created in MP2013 cannot be read in 2010 version. Depending on what data your maps contain you could try exporting and importing using the GPX file format. Another method I would suggest if you have both versions on the same computer is just a copy and paste of the data sets between 2013 and 2010.

More details on how to do that here: http://www.laptopgpsworld.com/5105-how-combine-pushpin-sets-different-maps-into-same-map
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