I was going to disagree with AerocatS2A's reply
The answer to the OP's question is very clear, NO, neither of the hypothetical pilots may claim the endorsement.
But for the original question I think he is correct.
However if the said pilot had a letter of appointment with the new company before commencing the training then he would be able to claim the expense.
The exact number of Virgin Blue pilots escapes me but it was not far off 500 pilots that were able to claim back the 737 endorsement costs.
As I mentioned the AFAP have all the details and funded the test case.
Previous posters advice of claiming the tax deduction without doing any homework and using the excuse of having made made a "genuine mistake" when they get audited is just simply insane.
The ATO have no snse of humour nor would the self assesment system work at all if it was up to the ATO to determine every claim and not have an effective penalty system in place.
The self assesment system works because of the threat of substantial fines and penalties if a mistake is made by the taxpayer.
Excuses of innocence, genuine mistake or deliberate act will be treated the same.
Talk to the AFAP to get the facts.