Why do they have to be "exactly the same"?
Sounds like you have an unreasonable boss.
Short answer is you can't have exactly the same boot drive. i.e. the same computer configuration.
Because the hardware will be different
If you have software that uses the hardware and software as part of the key to their licence you may find the programs won't work.
Create a exact copy of his desktop profile with the same software he uses now.
different computers but to him it will seem the same.
Problem with this approach
Every time he updates anything on his laptop you will need to sync it to the desktop.
That means the laptop needs to be plugged in for this to work.
You could use a program that communicates back to the host computer like PCAnywhere so the desktop computer is the master and all file alterations are done while online connected to this master. In this example the laptop is only the donor and is not really used except to dial or connect to the office to get to the master.
Another option is to use VMWARE and create a virtual computer.
i.e. will be exactly the same but same problem with file alterations, they will need to be copied every time.
So a better option
Use only a laptop with a "docking station"
He will have exactly the same things as it is exactly the same computer.
All the peripherals will be always connected to the "docking station" so he will never have to plug anything in just place the laptop on the docking station.
Another option is to use Terminal Server by MS or Citrix but these are expensive and complex systems to the novice.
The beauty of this solution is that you can have him log in from any computer that has some type of internet connectivity to a portal on your network which will give him exactly the same desktop regardless what computer he is on.
This option is by far the most expensive and is not generally done for just one person. Usually it is used for many to thousands of users.
Unless you are a large organisation then I see the best solution is to use the laptop with the docking station. If you have a network you might set up his laptop to backup while he is connected.