There are many types of memory - working memory, short term memory, long term memory. And each type of memory is different for visual and for auditory processing.
If time allows, I would recommend that you have someone do the psycho-educational evaluation in the country (and city) where you will be living. The results would be more relevant to the U.S.
You ask good questions; however, I cannot be specific. You need to sit down with the person who diagnosed him with an auditory processing problem and ask these questions.
It is good to consider early intervention. As a parent, it is within your rights to request a 504 evaluation for your child. This evaluation is free and will be conducted at your public school.
A school should not conduct an individualized evaluation of a child for purposes of diagnosing or identifying a disability without the written informed consent of the parent.