There is nothing special about a 'backup string' other than it should be setup identically with string silencers, etc. and shot in and tuned for nock height and brace height.
Initially, I just make or buy two strings and set them up, and once the first string settles to final length and is tuned for nock height and brace height, I remove it for a backup and install the other string and go through the same process. Next time, just buy one new string and set it up, then take it off as the backup, and put the old backup on.
As suggested, contact the bow maker to get the recommended string (material, strands, length, etc.).