One way you can do this is saving the terminal session into a file and then accessing that file with a browser. Since your question gives very little information about your setup, I will assume that i) you are connecting to *nix clients, ii) the client can serve a webpage.
The main tool here is a program called
script makes a typescript of everything printed on your termi‐
nal. It is useful for students who need a hardcopy record of an
interactive session as proof of an assignment, as the typescript
file can be printed out later with lpr(1).
You can install on Debian based distros using
sudo apt-get install script
Then create a simple HTML file on the remote machine with the following contents and save it as
output.htm (make sure it is accessible from the internet):
<meta http-equiv="refresh" content="2">
<meta> tag makes the page refresh every 2 seconds and the
<pre> tag ensures that new lines and spaces are displayed correctly.
Now, once you log on to the remote machine run
script -af output.htm. That will append (
-a) a transcript of your terminal session to the file
output.htm. Your client can then access
http://remote.server.com/output.txt and watch the commands as they appear.
If you use colored output in your terminal, the ANSI escape sequences that make the colors will be visible in your html output.