Pillow should automatically sync sleep session between the Apple Watch and the iPhone, provided that the devices can communicate (Bluetooth and/or Wifi are enabled on both devices).
This process can fail due to a miscommunication between your devices caused by watchOS issues. In most cases this can be resolved by restarting both your iPhone and Apple Watch.
As a last resort you can also trigger synchronisation manually as follows:
Open Pillow on the Apple Watch
Scroll down to the bottom of the main diary view
Tap on the "Settings" button
Tap on "Synchronize data"
Please note that syncing requires Bluetooth connectivity enabled on both devices while syncing is in progress.
If you are still experiencing problems please contact our support team.