@oscortega 

"QBO automatically categorized it as a "Transferred from Shareholder's Distribution".  Is this correct?

If not, what categorization should I use, so that I may associate the funds to the proper invoices?"

No, it's not correct. You should receive the customer payment on invoices and then match them in the Banking tab.

You will need to follow the following steps:

1) Since you've already automatically added the deposit to the wrong account category, you will need UNDO transaction from the register. Go to the "Reviewed" tab in the Banking and locate the deposit in question and select UNDO under the Action column. That will bring the transaction back to the "For Review" tab.

2) You mentioned payment on invoices. Go to Receive Payment screen (Create "+" New sign > Customers > Receive Payment) and select Customer and check outstanding invoices. The total amount received should match the bank deposit amount. Make sure to select the correct Bank account.

3) Go back to Banking > For Review section. You should see the MATCH sign for that transfer deposit. Once you click the match, it's done.

Hope this helps!