Q: Why can I receive iMessages only on my other iPhone? Two iPhones, one Apple ID, one number.

The setup:

Two iPhones (6S+ and 5), one Apple ID, one phone number. I use the same Apple ID on both phones. Both phones have parallel sim-cards using the same number. Both phones ran first on iOS 9.3 and later on 9.3.1.

The problem:

When someone sends me an iMessage to my phone number, the message is received only in one phone, but not the other. If I've observed the problem right, the receiving iPhones is always the one, on which I lastly activated iMessages (in the settings).

What works:
When someone sends an iMessage to my (iMessage) email, the iMessage is received in both phones. When someone sends an SMS text message to my phone number, it is received in both phones. When someone calls me on my phone number, both phones chime and I can answer on either.

What I've tried:
Made sure, that both iPhones have the phone number enabled in [Settings]->[Messages]->[Send & Receive]. Switching iMessage off and back on. Restarting the iPhones. Signing out of and back into iCloud. Resetting the network settings. Hard resetting the iPhones. All this on both iPhones multiple times and in different orders. Everything Apple Support person told me to do to the iPhones during a 51 minute call. Another pair of iPhones (4S and 5S) running iOS 9.3.1. Nothing has helped.

The questions:

Is anyone using a similar setup? Have you had the same problem? Did you solve it somehow?

ps:
I'm well aware, that the problem could possibly be bypassed by changing the setup (for example by using separate Apple ID's or separate numbers).
But I'm only interested in solutions to this actual setup (two iPhones, one Apple ID, one number). If you have it working on any version of iOS, please let me know.