Yes you can freeze canned mushrooms and they will be just fine.
But sometimes when you freeze canned mushrooms they may get mushy or soggy when thawed out but they still go well in soups, stews etc.
You can place a plastic wrap over the open can of mushrooms and use a rubber band to tie it on it and freeze the canned mushrooms in the can.
Or you can remove the can mushrooms from the can and put them in a freezer safe sealed container and they should keep for a year or longer.
It's best to eat the frozen canned mushrooms within 6 months to get the best freshest taste from them.
I've frozen canned mushrooms that I have opened and kept them for a year before I used them in soups.
But if I'm not using the can mushrooms yet I don't open them until I'm ready to eat them although I do freeze any leftover mushrooms if there's any left.