The duke, 62, wrote more than 700 words about his experience in the Falklands in posts on his ex-wife's Instagram account on Saturday - before they were hurriedly taken down.
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The musings were initially signed off as 'written by HRH The Duke of York', despite the Queen having stripped Andrew of his honorary military titles in January following the dramatic fallout from his civil sex case.
At the time, a royal source said Andrew, who was born a HRH, would no longer use it in any official capacity.
The 'HRH' was removed from the posts, before the reflection was deleted in its entirety two hours later.
In the first Instagram post, Sarah wrote: 'I asked Andrew this morning for his reflections on the anniversary of his sailing from Portsmouth to the Falkland Islands 40 years ago.'
Andrew's account begins: 'As I sit here at my desk on this cold crisp spring morning thinking back to April 1982 I've tried to think what was going through my mind as we sailed out of Portsmouth lining the flight deck of HMS INVINCIBLE.'
It concluded: 'So whilst I think back to a day when a young man went to war, full of bravado, I returned a changed man.
'I put away childish things and false bravado and returned a man full in the knowledge of human frailty and suffering.
'My reflection makes me think even harder and pray even more fervently for those in conflict today, for those family's (sic) torn apart by the horrors they have witnessed.
'And, i'm (sic) afraid to say, that the historical perspective my short war has taught me is this – war is failure to keep peace; war is failure of human judgement; war is failure to recognise we need to seek permission to understand another persons perspective or reality, whether or not we agree or disagree with that perspective or reality.'
Andrew also recalled being shot at, writing: 'I was flying and saw a chaff shell fired from one of our ships that passed not that far in front of us.
'For a moment it was on a steady bearing before it began to cross to our left.
'The terror that that was going to be that, just for a moment, has had a lasting and permanent effect on me.'