Pulling Information From A Column Based On Information In A Second Column?

Imagine I have 2 columns of information that look like this:

Column A
Column B

AS
Dog

AS
Cat

AS
Hamster

FT
Fish

These are my key columns. The letters are initials of people and the animals are the pets they're responsible for.

Now, I have 3 more columns that look like this:

Column D
Column E
Column F

These columns can go on for hundreds of rows.

What I want to do is pull out the information from columns D, E and F where the initials and pet match those in the key list, then paste that elsewhere (say to columns J, K and L).

So, for instance, the first entry would be copied across because, according to the key list, AS is responsible for a Dog, but the bottom entry for AS wouldn't because he was looking after a fish, and that pet isn't listed as one of his animals in the key list (Fish is listed alongside FT). Likewise, the entry for AH wouldn't come across because AH doesn't appear on the key list at all.