TL;DR

Forwarding messages across chats on Beeper Desktop and Beeper iOS is possible.

How to Forward a Message using Beeper Desktop

Forwarding a message in Beeper Desktop is as easy as pressing the menu over the message in question. Once the options are visible, press Forward Message, you'll see your message on the left side and the option to search for a contact or chat to forward the message.

How to Forward a Message using Beeper iOS

Forwarding a message in Beeper iOS is as easy as long-pressing the message in question. Once the options are visible, press Forward,  the option to search for a contact or chat to forward the message.