Put the related field on the layout of the first table, and search in it. It will be a bit slower than 'normal' searches as the field is unindxed.
I think you need a join table between table 1 and table 2. What if a check amount is not enough to fully pay off both/all properties to which you link it? It might be an amount that fully pays off one property and partially pays off another.
With a join table, you can list each property associated with that payment, but then also document what portion of the payment is applied to that one property. Determining whether or not the property is paid for in full is done by totalling the amounts in the join table for all such records linked to that specific property.