Sharing apple watch

Since the Apple Watch is paired to an iPhone with the same Apple ID, you would have to pair his Apple Watch to your iPhone, after your partner removed the Apple Watch from his Apple ID account.

Before you buy, sell, give away, or trade in your Apple Watch- Apple Support

Or you will have to use his watch and his phone, which will also record the data to his Strava app.

Since you installed the Strava App on your iPhone, you probably subscribed, using your Apple ID?

In that case installing the app on the other phone might not work, due to the different Apple ID.

Since unpairing the Apple Watch also creates a backup of the Apple Watch, it should be easier to pair the watch to your iPhone and unpair it after that, to pair it to your partners iPhone again, and choose the latest backup to restore the data and settings while setting the watch up again.

Back up your Apple Watch - Apple Support