Wash and clean the morels to remove grit, making sure to leave the morels whole.
Heat the oil and garlic until the garlic is lightly browned and caramelized, but not burnt. Add the water, salt, thyme, vinegar and pepper then bring to a simmer. Add the fresh morels and cook, about 3-4 minutes, until they wilt and decrease in size. Discard the garlic.
Place the morels and the pickling liquid into 1/2 pint or pint canning jars and process in a water bath canner for 15-20 minutes.
Small morels will yield the best pickles since they'll keep their firm texture. That being said, larger ones can still make great pickles too, but I like to cut them into pieces before adding to a dish.