Can MacBook Air 2012 storage go in 2011 Air?

I have two Macbook Airs. One is 11 inch from 2011, the other is 13 inch from 2012. I prefer the 11 inch but it only has 128GB which makes in nearly useless for the things I used it for. The 13 inch has 256GB.

If I open these up, can I just swap the storage chipboards? The iFixIt store sells different chipboards for them (though they seem to be identical in appearance).

I'm tempted just to go ahead and try but obviously don't want to do any irreversible damage.