Why wouldn't you try to contact the company or a place that sells its products for such information?

Best to ask here: https://hamptonbayfanandlighting.com/hampton-bay-customer-service/

Understand that Hampton Bay *IS* Home Depot.

To find another remote control, you might try registering a permanent search on Ebay for the model number of the gadget. Typically there will be a DIP switch inside the control, usually under the battery, that you set to match your present one.

Another solution would be to buy a new generic remote transmitter and receiver set, and get a second compatible transmitter, or an entire second kit if they don't sell just the transmitters. I see single speed kits for around $23 each and 3-speed kits for around $35 each at one of the big box stores.

Though as cheap as fans are these days, unless yours is top of the line, it might make more sense to just buy a whole new fan and get a second remote transmitter for it. You could donate the old fan to ReStore, Goodwill, or some similar place.