You have to check the webspace between the 2 App Service Plans. Are there identical?
You might move (multiple times) your App Service Plan to different Ressource Group but the webspace is based on your original Resource Group (when you created this App Service Plan the first time)
You might have also deleted your original Resource Group, so you might have to recreate it? (I have never tried this case, but it should create in the same webspace then)
To check I use PowerShell command:
Login-AzureRMAccount
Get-AzureRmSubscription
Select-AzureRmSubscription -SubscriptionId <Your Subscription Guid>
Get-AzureRmResource -ResourceId "/subscriptions/<SUB-ID>/resourceGroups/<RG-NAME>/resources" | Select Name, ResourceName, @{Name='webSpace'; Expression={$_.Properties.webSpace}} | Format-List
For the name space, you will get something like:
Name : Consoto_AppServicePlan
ResourceName : Consoto_ResourceGroup
webSpace : Consoto-SouthCentralUSwebspace
(Supposed that the location is South Central US)
So if you want to move your App Service to another App Service Plan name, you will have to create a new App Service Plan in the Resource Group named "Consoto" (refer to my example above) in the Location South Central US in the same subscription of course.
Then you will be able to use the Change App Service Plan functionality in the Azure Portal