Putpose is well to track the phones when abroad, and my HA is open to the exterior, via the http://myserver:8123 … that is why I changed the proposed URL from http://192.168.1.10:8123 towards the other one.
And yes, the full URL provided by the integration is something like this :
;-(
P.S. Companion app on the iPhone is only giving very rare updates, compared to the frequent updates of the companion app on Android, as I posted here :