E.C.
I usually handwash mine and then put them in the gentle spin cycle of my (front-loader) washer to wring out some of the water, then hang it up and it dries overnight.
The foam is EPS (expanded polystyrene) - the same kind that's used in bicycle helmets. You can call or email Britax to ask about whether it can be just stuck back in or post your q on a forum like this one http://boards.babycenter.com/n/pfx/forum.aspx?webtag=bcus... (host and many regulars are chid-passenger safety techs)