Use existing origination entity in a different US region

I have an existing origination entity in us-east-1 to send SMS messages vis SNS. Now I also would like to send SMS messages from SNS in us-east-2. But I get the following message while adding a new subscription in my us-east-2 topic:

An error occurred while attempting to add a phone number to the SMS sandbox. The phone number was not added. Error code: UserError - Error message: No origination entities available to send

The documentation is not very clear on whether one needs an origination entity for every region or per country. Am I getting the message because I would have to also register an origination entity in us-east-2?

And/or are origination entities not available in us-east-2?

Thanks!