'split' and 'cat' will work. Presumably there is no connection between the two computers, and no CD burner available - (otherwise, you wouldn't have asked, right?)
You can compress the file with gzip - but it's probably not worth bothering as at best, it might save you one trip back and forth.
Use 'md5sum' to re-assure yourself that everything was copied and reassembled faithfully - I once had to download a couple of Gb of data in 20Mb chunks. There was a mistake in one of them that 'ls -l' didn't show up but 'md5sum' did.