I have tried this and yes it does work. 2015 logic board is 100% compatible with 2014 (and therefore 2013) MacBook Air 11inch. All the parts were identical - aside from upgraded CPU, graphics and Thunderbolt 2! Adds 4k external display support (!), somewhat longer battery life. I'm very glad I investigated this before going with a 2014 board because this is a much bigger upgrade and prolongs the life of the MacBook by a good amount - this is the same as what they were selling in 2017 (2.2GHz i7). Many thanks to iFixit for the wonderful instructions w/ clear photos. Could not have done this otherwise - or without the iFixit tools. Pentalobe screwdriver, T5 Torx screwdriver, spudger. I had the tools on hand from a prior SSD upgrade (also thanks to iFixit) and figured they might be useful some day. Also thanks @danj for the advice and giving me the confidence to try something that wasn't well documented.