I have upgraded one leg of a work flight before (PHX - DEN in Economy, then DEN to SFO I upgraded to biz). They were married segments, meaning my departure airport is Phoenix, final destination is SFO.
It will reissue the receipt and keep the segments married together, showing the first in Economy, the second upgraded and usually have a note saying $X was collected due to fare difference and so forth.
What's wrong with just submitting the original receipt from the original booking? My company is not that airtight for flight receipts, so that's what I do when I upgrade any of my flights above coach. The only way an approver would really know, is if they call United and checked, or if your company has some sort of booking portal when you book your UA flight that has access to the real-time final receipts.