This is not address specifically in the official Fluxx FAQ

With the card as written in that edition, you should be able to do this.

It's worth noting that the word "exchange" doesn't matter here, because it's only used in the name of the card, not in the text of the effect.

Another card that has been renamed in newer editions shows that the name of a card is not important to its actual effect. After it has been played, the card "X=X+1" (later renamed "Inflation"), is actually now named "X=X+2". But the effect of that card is still to add one to each numeral, not to add two. So the fact that the card is named "X=X+2" doesn't matter.

So when you play the card, you simply follow the instructions as written, in order, which is to give a keeper to a player, and then to take a keeper from a player. Actually, assuming the card text is accurate in the Question, it doesn't even have to be the same opponent, you could choose to give a card to one player and take one from a different player.

However I believe that the fact that the newer printings of the same card have changed the wording such that this interpretation is no longer possible, I don't see a good reason to choose to play with a card as written, instead of playing with the card as intended. The fact that the wording has been changed is clear indication of the intent of the card, and while Fluxx doesn't have as clear-cut rules about things like errata compared to something like Magic: The Gathering, I believe that for the sake of understanding rules in general, the most recent official version of a rule should always be considered to be the only one that matters. Playing by an older version of a rule is the same as playing by a house rule.

This is not address specifically in the official Fluxx FAQ

With the card as written in that edition, you should be able to do this.

It's worth noting that the word "exchange" doesn't matter here, because it's only used in the name of the card, not in the text of the effect.

Another card that has been renamed in newer editions shows that the name of a card is not important to its actual effect. After it has been played, the card "X=X+1" (later renamed "Inflation"), is actually now named "X=X+2". But the effect of that card is still to add one to each numeral, not to add two. So the fact that the card is named "X=X+2" doesn't matter.

So when you play the card, you simply follow the instructions as written, in order, which is to give a keeper to a player, and then to take a keeper from a player, who now has the keeper you gave them.

However I believe that the fact that the newer printings of the same card have changed the wording such that this interpretation is no longer possible, I don't see a good reason to choose to play with a card as written, instead of playing with the card as intended. The fact that the wording has been changed is clear indication of the intent of the card, and while Fluxx doesn't have as clear-cut rules about things like errata compared to something like Magic: The Gathering, I believe that for the sake of understanding rules in general, the most recent official version of a rule should always be considered to be the only one that matters. Playing by an older version of a rule is the same as playing by a house rule.