If you are trying to replicate exactly the fingering in your chart at the 12-th fret and beyond it may not be possible. By the way the fingering you have is only one of a few ways to play it. You can bar the three notes with the first finger and either avoid playing the high e string, use the pinky on the 5-th fret e string to get another A. You can also finger those notes in the following sequence on the second fret (1, 2, 3), (2, 1, 3) (as you posted), (2, 3, 1) (which is Amin with the index finger pulled up a fret). etc. There isn't a perfect or proper form here. Any of these are necessary for smooth motion from one chord to another within a progression and I've seen all of the above and more notated in classical and jazz guitar arrangements. That being said, perhaps don't try and replicate the exact form. If you want to really hear the voicing
(x, 0, 2, 2, 2, 0)
on higher frets you will have to work at it until it feels comfortable. I personally do not use a capo and would bar the first finger to get the highest and lowest note in the chord, then use either a bar with the third finger to get the other notes or some combo of (2, 3, 4). That being said the open string fingerings do not survive when they are moved up the finger board. The voicing can be preserved but the fingering cannot (at least not easily without a capo). For example the A-form you want to move would be fingered as (x, 1, 2, 3, 4, 1), were the 2, 3, 4 fingers are all on the same fret consecutive strings. For this reason a lot of players prefer to use the "movable" chord fingerings in the open position. For example you can play the open A-form as (x, 0, 2, 3, 4, 0), rather than (x, 0, 2, 1, 3, 0) or other. This way as you shift your hand feels the same. It's one option.