Odd choice, normally a service would be running constantly in the background, in this case it would effectively run once and then not really sure what it would be expected to do :confused: Does your manager actually have a reason for wanting a service?
Try this instead, start -> run and enter mmc
File -> Add remove snap-in -> add -> select Group Policy Object Editor and click Add, Finish, Close and then OK. Expand Local Computer Policy, Computer Configuration, Windows Settings and select scripts.
On the right double click startup and then select Add... then Browse...
In the window that appears right click and create a new text file and rename to something useful like mapdrive.cmd and open it in your editor of choice and in it enter something like
NET USE \\\
then save and exit that and keep accepting, okaying etc. till everything is done.
If you are not overly familiar with the NET USE command then drop to a command prompt and just type
NET USE /?
for a bit more help (like specifying a user / password when mapping)