I'm not Alaskan but we have the same climate and same morels.
There are several groups of morel species and their fruititng patterns/seasons are different. You need to remember that when planning your foraging.
The morel in Thurman's photo looks like a yellow morel (used to be known as
Morchella esculenta, but there are several species). It is not a burn site morel although they do appear after fires sometimes, just not in great numbers. At ~55°N + continental climate, they start fruiting much earlier than burn site morels, usually in the beginning of May, and are good to collect for about two weeks until they're overgrown or destroyed by maggots. Black morels of the
Morchella elata group (also a bunch of different species) follow a similar fruiting schedule. There are no reliable ways to predict good crops of these morels.
They are usually big enough to collect when bird cherry begins to bloom.
True burn site morels appear later in the season. The black-footed morel,
Morchella tomentosa, usually starts fruiting in the very end of May or early June following a low-intensity forest fire the previous year, and fruits for a couple of weeks.
Another burn site morel,
Morchella capitata (plus a couple of visually indistinguishable closely related species) appears another two weeks later, so it's not uncommon to find them in late June or early July, depending on your latitude. They're probably the best morels, big and fleshy. I think milkcrate's morels are from the
M. capitata group.
this is a young
M. capitata with a black morel (smaller but older; all other black morels around had already rotted down). Young burn site morels of the
M. capitata group have a peculiar silvery powdering on the "honeycomb" ridges, from the translucent lightbulb-shaped cells they're covered with.
Like people here said they produce a bumper crop the year following the fire and then disappear. You might find a few two years after the fire but it's usually not worth the effort, with all the nasty tangled fallen trees, soot and bears eating young fireweed.
If you collect thimble morels (which are a very popular edible here, and are good eating as long as you boil them first), start very early. They start appearing when buds pop on their host trees (aspen and cottonwood, as well as bird cherry, mountain ash, and crab apples). False morels (Gyromitra) appear simultaneously but I wouldn't recommend eating them unless you know how to cook them. They're absolutely safe after drying, too.
At higher lattitudes (~°60 N and above), everything shifts to about 1.5 weeks later. Shady, cool places such as north-facing slopes and ravines add another week or so. Elevation is also a factor.