I took a read of the service manual. I could have missed it, but I see no reference to any battery. Most likely a capacitor should keep enough charge on the memory to stop it dying, but has likely deteriorated over time.
As an alternative suggestion, maybe he could put a UPS on it (and any other music/computer gear he uses) in case of a power outage, and simply never turn it off?
It’s not like it draws much current, wouldn’t cost more than pennies a day to keep it switched on.
His main problem is, putting it in to a repair tech to sort the problem out might cost more than either finding another PSR1000, or even something FAR more modern and capable, with USB backup of the memory. Cheapest solution I can think of is simply to leave it on 24/7!
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An arranger is just a tool. What matters is what you build with it..!