How do you install wall mount mailbox into brick house?

Make a new hole in the wall; the old one will be covered by the box. Depends to some extent on what the wall is made of, though. Can you drive a screw in and get it to hold, or do you need to use a plastic wall anchor?
If you're happy with the old location, start one screw in one of the old holes to begin with, just to hold the box in place temporarily. Level the mailbox, and mark the hole location of the other hole on the wall with a marker. Then swing the box out of the way, or take it down, drill a pilot hole for the other hole's screw. If required, insert a plastic wall anchor there, suitable for the screw you're using, then reposition the mailbox and insert screws.
If it's a masonry wall you'll need a masonry bit to drill the holes, and you'll have to be careful to line them up well. In that case, you might be just as well off back up the inside of the mailbox with a block of wood and drilling a new hole in the back of the mailbox to line up with the old hole. Just measure carefully, and use a center punch or nail set to make a dimple before trying to drill a hole in the metal.

I hope this information allows you to resolve this issue. If you need further assistance, please post back with a comment to this thread.
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