Well, update on this matter:

There is no information on aa.com about boarding passes - after logging on with the PNR, the following options are displayed:

Same-day flight change
Email trip
Send to calendar
Print trip and receipt

No boarding passes. Again, on JAL's website there is no option to log on either because I do not have JAL's confirmation number.

Hope that my wife will get boarding passes at SQ's counter tomorrow morning. Otherwise I would consider that it is big fail.