“Internet” communication has been around for an alarmingly long time; it just wasn’t adopted until much later.
The fax machine was patented 20 years before the US Civil War, and was used in France in 1865. Yes, the first fax was sent before the telephone was invented. 100 years passed between the first fax being sent and the first consumer fax machine to be sold. Wiki
Neat video! Thanks for sharing 
yeah surprising enough the earliest “internet” (darpanet / bitnet / USENET / UUCPNET) was all store and forward p2p networks centered around fido/uucp/ftp.
Heck the original [RFC]'s where just email message threads that literally where requesting peer review of proposed protocols for ARPANET that one would actually copy from an ftp server.
Thanks to the switch from NCP to IP/TCP on APRAnet in the early 80’s the work of CERN, Eric Allman, and University of Minnesota we got http/html, smtp, and gopher retrospectively.
So yes, the first fax was before the first telephone and the first email was before the tcp/ip servers (pop3/imap and smtp).