Right click on the pushpin set in the Legend and select "Export to Excel". And then you can re-import using the Import Wizard.
Also copy & paste might work - it is worth a try as some parts of maps do know about the clipboard. Select the pushpinset in the legend, and then try CTRL-C for Copy. Then CTRL-V in the destination map for Paste.
Richard Marsden
MapPoint Add-ins at Mapping-Tools.com