Hard to tell from the picture if the insulation is just enough to cover the gap between the door frame and the stud or if there is a major gap. Typically, the door studs will be oversized just a bit to make it easier to insert the prefab door & frame into the opening in the wall where the door goes. The amount of the oversizing depends on the measuring for the height and width of the opening versus the prefab door frame as well as whether the studs and floor are truly level.
This is why the previous posters were recommending that you take some shims with you because you never know how much the gap is going to be. Shims are a quick way of taking up that gap between the studs and the door frame to make the door frame installation that more secure.
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It can be a PITA to hand nail and get the shims just right. So....my suggestion is to buy some trim screws that won't look terrible, but would allow you to back the screw out and try again if you see them pulling the door frame too far away from the door.
Be sure you have the correct bit to drive these or check the trim screw package to see if it includes the correct bit. Also...predrill the hole so the trim doesn't tend to split.
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Moving on to the door latch, typically there are only two short screws holding the latch to the prefab door frame. The screws are short because they are shipping these door assemblies and don't want any protruding screws to stab someone.
When it comes to the actual installation of the door, the finish carpenters typically set the door in the wall opening, tack it up more or less level and plumb.
A better finish carpenter will take time to shim the door frame, but take out those short latch screws and install longer screws that will secure the latch to the stud.
The BF was able to kick the thing in because the door only had the two short screws that didn't reach into the stud.