Weird iMessage behaviour mirroring between iMac and iPhone

[Tumbleweed666]

Got a new iMac, everything seems to have transferred ok from the old one
One thing, when i get imessages to my phone they all turn up on my iMac. As expected. Except for just one sender.
And as it happens that's slightly inconvenient.
The only distinguishing thing about this sender from others is that its likely not an iPhone but a computer system using a service (as these messages are from a company)
But it is sending to my mobile number.

Any ideas?
TIA

 

[Popple]

Make sure you have Text Message Forwarding turned on on your iPhone. Settings > Messages > Text Message Forwarding > select your new iMac.