Yes, I now I understand where you're coming from. On older home routers (like the Linksys BEFSR41), you only had the option of setting DHCP or static, but not both - this is one of the most basic routers out there.
Even if you do have an older router like that, you can still do what is described above. You can configure a router to pass out IP addresses (DHCP) or have you manually assign IPs (static). You can configure a PC to automatically get an IP from a server (DHCP) or you can manually assign the IP (static). There are options on both the router and the PC for this, and they don't necessarily have to match to work.
The router will be able to route to and from anything that is a) on the same subnet as one of the router's interfaces, and b) uses that router as the default gateway. So if the router's IP address is 192.168.0.1 and it uses a subnet mask of 255.255.255.0, then you have 253 other addresses on that subnet that will work with the router.
On some routers you can manually configure the IP addresses used in the scope, or set exclusions on IP addresses that you don't want the router to assign to devices. Even if the DHCP server doesn't pass out those IP addresses it will still be capable of routing traffic to/from those addresses, so long as it is on the same subnet. So you could set the DHCP scope to be 192.168.0.20-192.168.0.254 and have 192.168.0.2-192.168.0.19 free to assign statically, which is what was suggested here.
If you cannot configure the DHCP scope on your router, a somewhat ugly workaround that should suffice would be to assign static addresses to devices from the upper end of the DHCP scope (192.168.0.254, or .253, etc) since it is unlikely that you would have 200+ devices on your home network. In the case above he can probably still get the same effect with using the .13 address if he has fewer than a dozen devices on his home network.
Alternatively, he could switch his entire network to static, then statically assign everything. This isn't much of an issue if you only have 1 or 2 devices to configure.
However, I think that the best solution for this particular issue is probably just to set up profiles on the laptop so that it is DHCP at home and static at work. Assuming that he has the correct permissions to do so, which he may now.