In exceptional circumstances with very well behaved data you might get away with this in one model using the floating trap, some calculated fields and a summary - if you can post samples from the two reports here between and tags I could let you know if there's a chance of that approach working.
But if you have Monarch Pro, then you can do this easily with a two-stage approach. Open Report A, and trap your data, and export the table to an Access file (.mdb extension). Then close Monarch. In another Monarch session, open Report B, trap the data from this, go to the table window, and select Data > External Lookups, and define a new external lookup to the Access file created in the first stage.
Join the datasets on the invoice number and select the required fields.
A quick question.
Are you able to treat one of the reports as the 'Master' report and the other as the one you want drag the extra field from? If so the extract from the non-master report and using that as a look up is the way to go, as Olly said.
If, however, you need to include invoices (by number) that don't exist on both reports but still need to be listed, then a slightly different approach would be required. Same principle of a multi-step process though. Probably ...
I'll assume you have scenario 1 but if it is more than that let us know and we can come up with some further ideas.