One more time....

RenjolynC - respectfully, your answer in unhelpful in two significant ways:

1 - Sending us to your colleague Charies_M DOES NOT get us to useful information. It gets us just to Charies_M's long list of posts, not to a relevant answer.  Once I'm in Charies_M's thread, even searching for "Transaction List by Customer" doesn't get to anything useful.

2 - Transaction List by Customer CANNOT be customized to provide the needed information without a MANUAL WORKAROUND at the time payments are entered.

iow - your answer is incomplete and unusable.  It's rote regurgitation. 

For those of you playing along at home, I've beat the snot out of this problem.  The ONLY way I've found is to manually enter the invoice numbers in the memo field in the Payments screen.  Then and only then can you display the number of the invoice paid in a Transaction List by Customer.  In the attached image I've customized to provide the title I need, but the report originated with Transaction List by Customer.

Intuit peeps - the reason this is insufficient is that it relies on manual entry.  Manual entry means opportunity for error - transposed number and other brain farts.  I've caught myself entering the check number there...