Moving over your existing Health and Activity data from your old iPhone to a new one can be a tricky business unless you know exactly what you're doing. The problem stems from the fact that Health and Activity data is not stored in regular iTunes backups, which are unencrypted by default, unless you remember to turn on encryption manually. It's a security precaution to prevent malicious users with access to your computer to mine your sensitive medical data from unencrypted iTunes backups.
The approach also poses a major challenge to folks who log their fitness and health data in Apple's Health and Activity apps. Surely you don't want to start from scratch and lose all the Health and Activity data that you'e amassed in the past year or so.
As it turns out, there is a way—actually, two ways—to preserve your complete Health and Activity data logs when you switch to a new iPhone.