Session Logging stops when using "screen"

When I use the screen utility (see below) no output is written to the session log.

This may be the expected behaviour of screen but my expectation is that everything that appears in the Xshell terminal window is written to the log file. I know that I can capture the output of the entire screen session on the remote server but this is nowhere near as useful to me as Xshell's local logging, i.e. dated, consistent file names, no need to remember to log every time I start a screen session, etc.



Installed Packages
Name : screen
Arch : x86_64
Version : 4.0.3
Release : 18.el6
Size : 795 k
Repo : installed
From repo : rhel-x86_64-server-6
Summary : A screen manager that supports multiple logins on one terminal
URL : http://www.gnu.org/software/screen
License : GPLv2+
Description : The screen utility allows you to have multiple logins on just one
: terminal. Screen is useful for users who telnet into a machine or are
: connected via a dumb terminal, but want to use more than just one
: login.
:
: Install the screen package if you need a screen manager that can
: support multiple logins on one terminal.

Program Ver. : Xshell 5