Exchange Partition

I have a rather large partitioned table which gets new data several times a day.  The developers have created a process where they build an unpartitioned table (with the exact same columns) and manipulate the data until it is finished being processed.  Then, I need to add the data in the unpartitioned table to the partitioned table.  There are several options available, but the exchange partition seems the fastest. 

 

I have no problems moving a partition out from a partitioned table, but I cannot figure out how to move the unpartitioned table (segment) to be a partition in the partitioned table.  I’ve read that it is possible, but cannot find an example anywhere.