Worse case you can just hand stitch it with a good rugged poly thread. But like everyone else said - anyone building gear, and I know fin does, can stitch a strap in a jiffy. No big deal.
DIY Gear Supply - Your source for DIY outdoor gear.
If you were to offer to pay for the damage, it might be a good excuse to upgrade the suspension. A few dollars towards some fancy lightweight slings for instance.
Ful, in the meantime, you can always tie a knot in the webbing so your not stranded. It'll work till you can get it properly fixed.
Fin's a top-notch guy, it will be okay.
Ambulo tua ambulo.