Pillow should automatically sync sleep session between the Apple Watch and the iPhone, provided that the devices can communicate (Bluetooth and/or Wi-fi 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 synchronization 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.