In a price-list from April 1939 for the HJ no button with an "A" was included, just the numbers and the "S"-button.
Nor was the "A" included as an addendum to the price-lists from the RZM until late 1942.
I cannot find a definitive solution, but it could be used with the shoulder-straps for the Akademie, or as mentioned
Ausland, as the letter A was also included with shoulders-traps for some of the Deutsche Jugend outside German
borders, as Croatia etc.
With some organizations as for example the SA, the "A"-indication stands for Ausbildung, but I have never heard
about such for the HJ. But who knows, as there is still a lot not revealed!
For me the A does not belong to the number 61.