If you have figured out how to link the two tables, you must have gone into relationships and made a relationship between the two tables. I assume that the field on the right hand side of the relationship is your project number field from the table A (and not the generic Related project number] field which would require you to maintain the links manually.
Then just go to that relationship and on the right side you will see a button to add lookup fields. Use that to pull in any fields that you need from the parent down to the child.
