You can leave them where they are and they'll flower next spring. No need to put them in pots.

I agree,and any straggly shoots can be cut back to lower new growth,if you can see some..or just cut them off if they don't look strong and healthy....mine have been in a few years now,but I take cuttings of the new top growth,for the next year as well..

Are we talking perennial wallflowers here or the biennials? The latter should be pulled up and composted, the former - well, mine anyway - are still in flower, and should, as Bloomer says, be trimmed and left where they are. I would guess they will be biennials, as the perennials are rather expensive (unless you take cuttings and propagate your own) and 15 of them would constitute a VERY generous gift.

Biennials can be left in but seldom do as well as in the first season. I compost mine and buy a new bunch of bare root wallflowers in the autumn. They are available quite cheaply at garden centres and some greengrocers or florists. The trick is to make sure they look fresh and plant them the same day! If short of space you can put them in a little trench somewhere out of the way for the winter and then plant them where you want them in spring. They need a bit of protection from slugs.This system works for me.