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Hadn't thought of this - wash your hands of it. He can decide if he wants to keep reinvesting dividends
I know he wouldn't be inclined to keep track of the cost basis going forward, but without reinvesting he wouldn't have to.

You're already giving him his annual 1099-DIV and letting him do his own taxes. If he's that much of a responsible adult, he can keep track of a single DRIP account.

For myself, using Quicken seems like a pain. For a specific task like cost basis of a DRIP account you can suggest that he just:
1. Keep an old-fashioned paper file with your year-end statements (or quarterly, if they don't give you an inclusive annual statement.) You should be doing this, along with your Quicken data, for substantiation. Give it all to him.

2. Keep a running tab of the cost basis on an Excel (or similar) spreadsheet. This will come in handy if he makes a partial sale.

If you or he have never sold shares from this account, you have probably assumed that shares would be sold on a first-in, first-out method (or specific ID, method perhaps, if the custodian is cooperative.) For shares acquired after 2010, an average cost method can be used, which was previously available for mutual funds only.

Regardless of the method, for purposes of partial sales, a spreadsheet can work better than Excel in coming up with the right cost of shares sold, better than Quicken, at least as far as I can imagine. Of course, if the entire batch of shares in the account is sold, the total cost is the total cost, and you can enter it all on one line with "various" for date acquired. Except, of course, for shares acquired less than a year ago, which are short-term.

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