You can fix into the frame, it is likely reinforced with steel, so you would drill a pilot hole slightly smaller than the (self tapping) screw diameter. Use an hss bit. If the angle is wrong you could pack out the gap with plastic shims or the like. But you could better use what appears to be a flat section between the frame and the coving, if that is too small you could replace the relevant section of architrave with a suitably thick piece flat piece of timber and fix to that.