Yes indeed parrots have very long memories. I have heard many stories similar to yours. I'm sure they remembered their old friends.
About six months ago, I gave two budgies to my friend and I still kept four. I had them for about two months. Now, I am babysitting them for two weeks and my budgies fell in love with my friend's. They are all preening each other and everything. Could they remember the other budgies from so long ago? Didn't seem normal for them to get along so well so soon.