Battery replacement for iPhone 1?

I doubt you can. Apple won't have batteries for a phone that old, you might try Batteries + if you have one in your area or call around to repair shops that work on iPhones and see if they might have one.

The original iPhone was discontinued a bit over 15 years ago, so it is likely that Apple no longer offers battery replacement service for it. During that time, cellular networks have changed drastically, so even with a new battery, it probably wouldn’t be useful as a phone now - just as an iPod Touch.