You can easily request to export your memories from your BackThen App.
Please make sure you are running the latest version for your BackThen App.
Step 1: Tap on the menu button at the top left of your timeline (circled below)
Step 2: Tap on 'Export Memories'
Step 3: Finally tap on the download button next to your child's name.
You'll be able to download all moments for all your children.