Couldn't he weld the, presumable, thermoplastic too?
What I found exceptional for this kind of small plastic repair is one of those welding guns that can hot-staple, originally a professional tool to repair plastic elements like bumpers in car body shops, they are now available cheap (from China, quality may vary), still makes no sense for just one repair, but it is an useful tool to have if you happen to do repairs often.
another approach I've had success with is using a little aluminum sheet over the break and pop rivets on both sides
Answering your actual question, if you are on the US West Coast, TAP Plastics might be a good source if they are near you: https://www.tapplastics.com/departments/fiberglass. If you are elsewhere in the US, either TAP or https://www.jamestowndistributors.com/product/fiberglass-and... online would be good places to start. If you are non-US, you'll need to provide more info and hopefully someone else can advise.
It is however possible to do this kind of repair with fiberglass if you drill a few holes just over and under the crack.
The resin will get into the holes and keep the inner and outer fiberglass layers together, besides acting as a sort of nails transmitting the forces applied to the basket to the outer fiberglass layers.
But unless you are familiar with fiberglass and have the materials from another project, it makes little sense, you can have the same result (with the same technique of drilling a few holes) using metal epoxy putty, the kind that you cut a piece from a stick and knead/mix in your hands.
Honestly, it's unlikely to be cost-effective on a $4 laundry basket. But if you happened to have all the materials around from doing a different, larger project you might use the leftovers for a repair like this.