Done this before, and yep, they'll need AY to issue the BP's in HEL. AY had no problem doing this for me. And yep, the BA person at the "transfer" area will need to see these to let your people thru the corridors.
If your people are AA Plats or higher, I'd def. recommend a stop at AY's lounge in HEL. And, the AA flight is significantly delayed, I'd suggest a stop at the BA Terraces Lounge in MAN, as it def. beats the term. area downstairs. But, that's only if time permits...the time they've got as is may be too tight for the lounge visit.