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Since watchOS 5.1 and iOS 12.1 release (October 30, 2018), some applications are no longer installed on the AW S4 from an iPhone 6 Plus.
I spent 3 hours with a Genius in the Apple Store without it being able to solve this issue.
I have found this thread on Apple forums :
For workaround this issue, I use the free version of iMazing 2:
Install iMazing 2 on your Mac or PC and plug your iPhone in USB.
Select your iPhone in availaible device list on the left and click on « Manage Apps » in the right column.
This window appears:
Right-click on the application that does not work on the watch (Messenger by example) and, in the menu, click on « Install to Device »:
Login with your Apple ID to download the application:
The application is updated on the phone. No data is deleted or lost:
After installation, the app is « cleaned » and a blue dot appears on the left.
You can now install the app on the watch:
And that’s the result: