Chosen Solution
I recently ordered an A1466 battery but I got an A1405 battery sent to me instead. I’m not keen on getting an exchange and was wondering if the A1405 battery would fit in the A1466 MacBook Air.
Not sure why you got the older A1405 version of the battery which was introduced with the 2012/13 system. It is physically the same but it is based on an older chemistry than the newer A1496. So it will work in your system. But it won’t offer the same amount of run time (maybe ~10 min less).