I would credit it to the AAdvantage account. I would not bother with JAL's Mileage Bank as the points accumulated will expire in like 3 years with no way to extend it beyond that.

I learned the hard way several years ago when I flew on China Airlines and banked my miles from those flights into CAL's Dynasty Flyer rather than Delta Sky Miles. I accumulated over 50k and lost all of it those miles these past 2-3 years! I just stick with Oneworld using AAdvantage, Star Alliance using United Mileage Plus, and Skyteam using Delta Sky Miles, at least with the latter two miles never expire. AA's you can keep extending and accumulating/banking miles as long as you have activity or fly once on AA or Oneworld partner flights in 18 months.