Updating multiple phones-can you copy file iPhone 3G

I have two phones, each matched to its own computer. Both phones are of the 3GS variety, but one is an 8GB the other a 32GB.
Can I download the 4.2 update on one computer, then copy it and insert it into the right folder on the other computer to avoid having to download it on both computers?
MBP 15-inch 2.66 GHz Intel Core i7 / 4GB SDRAM / AG Screen (Mid 2010) Mac OS X (10.6.5) iPhone 3GS (32GB), AEBS DB II (Late 2009), Apple Wired Keyboard/Mouse, ClamXav