How to add my app to “Share With” menu?

I’d like to be able to add my app to the list of apps in the iOS “Share With” menu. Is this possible with apps that aren’t written in Swift? If not, would it be possible to write just the “share with” functionality in Swift and use (e.g. a RESTful API) to integrate with it? Can anyone point me toward resources that covers this? Thanks for your time and consideration!

How to add my app to “Share With” menu?
 
 
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