What can be substituted for the fish sauce for vegetarians?

You can buy vegan fish sauce at Whole Foods or Amazon. I haven't used it, so can't tell you anything re. taste.

Make a sauce of dried shiitakes and soy as a substitute.

Not exact replacements, but with similar amounts of umami -
Soy or tamari sauce
Vegetarian Worcestershire sauce
Mushroom soy broth, as in this article:
https://food52.com/blog/22057-how-to-substitute-for-fish-sauce-in-a-pinch