I doubt you will find a shop that will do this, and if you do I'm sure they'd charge much more than you could just buy a used 2300c for. The upgrade used to come with a complete bottom half, and they'd move over your screen and hard drive. The 2300c screen is a bit larger but has the same 640x480 resolution.
I'll also chime in and say that unless your friend needs to use PPC-only software or an OS greater than 8.1, the upgrade is not worth it. I used to own a 2300c and I sold it and bought a 280c which is much faster for the older 68K software I was using (Word 5.1 and so on). The 2300c is a very disappointing machine speed-wise, though the IDE drives you can use are much cheaper.
If your friend still wants to do it, I'd recommend getting a broken-screen 2300c on eBay, or even easier just buying a complete 2300c and selling (or just keeping for backup) the 280c. Any 2300 motherboard will work with any duo screen (even the old passive matrix ones) and either IDE or SCSI drives. If you've tinkered with the insides of macs you could do the swap yourself but duo guts are tricky and there are plenty of stupid little plastic tabs and so on that can break off and cables that can get pinched, so it's a bit of an advanced job, though not too scary if you take your time and get the service manual (online in various places).
I sped up my 280c a lot by putting in the max RAM (40M) and then using a RAM disk to run System 7.1.1. That was probably the fastest Apple laptop till the 1400/133's came out!