Is there a way to snap the currently open tab(s) on Firefox (or any other browser) on Linux?
I have full user access to that machine...
If by "snapping" you mean transferring one tab from one process on machine A, to another process on machine B, then no, you can't do that.
Here's a strategy:
Use ImageMagick's import command to "snap" the currently open tab:
$ import -windowid $window_id tabNNN.png
Use some scripting to ask the browser to go to the next/previous tab in the list of open tabs. You can use xdotool to simulate the key presses or do a remote connection to the browser (chrome allows you to do this).
Repeat from step 2.
Here's a one liner that captures all open windows in X:
$ for i in `xdotool search .`;do import -windowid $i $i.png;done