In Powershell when we would like to create a WebApp, you must specify a Service plan :
New-AzureRmWebApp -ResourceGroupName $RG -Name $WEB_Frontend -Location $location_west -AppServicePlan $APP_Service_front
But, if the service plan is in another RG, Azure will create a NEW Service plan in the same RG of the WebApp, this is problematic …
The solution is to specify the service plan ID with :
$APP_Service_front = (Get-AzureRmAppServicePlan -Name $APP_Service_front).Id
And now, the WebApp will be using the new RG and the service plan will stay on the another RG.