Hello,
Module ActivityReport is very generic. It's purpose is to allow administrators to track user (employee) activity in the system, to see if it's properly used and if users are using the system actively.
It should not be used as a tool to display who finished a task or made a phonecall - for that the best tool is usually an applet or Calendar.
That said, it's possible to modify ActivityReport, albeit it's not an easy task. All the code needed here is contained in ActivityReport module and it's a pretty small one.
You should go through the basics included in this tutorial: http://www.epesi.org/index.php?title=Epesi_tutorial
With knowledge included there you'll get to know how epesi works, what is a RecordSet, crits, how to create/modify a form. You should be able to start on adding the feature you want and if you get any problems along the way, feel free to post here.
Kind regards,
Arek