what would be the fastest way to create an app that integrates to the "share" box of iOS?

You need to create an app extension, in your case a share extension. I don't get the "fastest" part of your question since I don't see another way to do this. I might have misunderstood your question though.

@marie_dm - Thank you for replying!

TBH I've never developed for iOS and I don't want to be an iOS/Swift pro. I just want to develop this share extension you mentioned in the most hacky & fast way possible.