It doesn't matter where your code is running... even somewhere not part of AWS. Most services, like SNS, have a regional endpoint That you need to access, in order to connect with resources defined in that region. That's what the AWS console is doing, behind the scenes.
If you are using an SDK or another library, rather than using your own code to directly communicate with the AWS services, then what you're looking for is how to change or set the "region" or "endpoint" with the request or (likely) in the constructor.
You can only send requests "from any other region" in same sense that you can send requests from the Internet, generally. You don't send them through the other region's SNS endpoint. You connect directly to the target region.
Note, though, that the SNS SMS solution is of somewhat limited utility -- useful for notifications to groups of individuals who are expecting your notifications ("The nightly global batch process has completed, but errors were encountered.") but not so much for customer contact ("Your order has been shipped.") since the topic subscribers are not individually addressable... send to one, send to all... all who responded positively to the subscription confirmation message, that is.