The notion that you would split checks into two different tables suggests that you would be very wise to research database normalization. Here is a page that contains a lot of subject matter on db design that you should start with - http://www.fmsinc.com/free/newtips/primarykey.asp Look at the topics in the nav pane on the left.
Your initial table can do this with a field that 'flags' the check as received. This can be as simple as a checkbox field, or a word such as "Received". However, if using a text value, I'd consider implementing some sort of process control so that users cannot introduce typos, which would cause a query to not return rows. This could be a combo box in your form with a value list so that you avoid misinformation.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.