Pair Google Home (mini) with Harman Kardon Invoke

So we have this Harman Kardon Invoke, a smart speaker with Microsoft Cortana. For me as a non-US-user, it's a rather limited device. So trying to find the best use, i wondered if i could pair the Invoke with a Google Home via Bluetooth (BT), as to use the Invoke as BT-speaker.

I did find instructions of how to pair the Google Home mini to a BT-speaker, but the Google Home app seems to have evolved since that documentation was, so here i document how to pair a BT speaker:

• open your Google Home app
• go to Account, the icon of a little person in the lower left of the home screen
• click the GH device you want to pair (i only had one at this moment, so i clicked '1 local device'
• in the next screen, click the device itself (again)
• in the next screen, click the gears icon in the upper right
• you should be in 'Device Settings', a long list of settings. Look for 'Paired Bluetooth devices'. You should see a sub option ''.
• If you've never paired the Invoke: press the BT pair icon on the Invoke. Your Invoke should show up in the GH app. Click it
• If you've paired the Invoke before: click your Invoke

Currently, i have not found a way yet to keep the BT-connection survive the GH turning off (for the night) and on again. So i need to press the BT pair button on the Invoke every time i want GH sound to go over the Invoke.

Invoke review:

• we find this Invoke activates Cortana with 'false-positives' (activating it while nobody says Hi Cortana) than the Google Home and Amazon Alexa ... especially when the TV is on ...rather annoying, especially when Cortana starts responding to what it thinks it heard ... 
• it has no open API whatsoever, so no way of having it play nice with other smart devices via Home Assistant or something
• there hardly seems any development going on ... another Microsoft graveyard product? And Harman Kardon not feeling responsible for that partnershop and customers? But reading this, let's hope at some point, something new will arrive and they won't forget the current customers
• very limited set of services