Store extended properties and apply to another copy of the database
I don't know of an easy way to just extract them and reapply to another target, but you could use the data in sys.extended_properties to generate a script to add the properties to another database using calls to sp_addextendedproperty.

See https://msdn.microsoft.com/en-us/library/ms177541.aspx and https://msdn.microsoft.com/en-us/library/ms180047.aspx for a bit of documentation around that.

If the target database may already contain some properties (from earlier transfers, or added for other reasons) then the script you generate may need to be more clever and check to see if it should call sp_updateextendedproperty instead (also potentially sp_dropextendedproperty to remove properties that are now deprecated).