From the Nürnberger Hut, continue to the west following the trail the ascends immediately from the hut. At a junction, follow the trail to the left (alternate route described below), signed out for Niederl (mountain pass). Continue ascending steeply, arriving at another steel cable passage shortly before the mountain pass.
From the mountain pass, descend a cabled section toward the small lake below. Continue to descend gently from the lake, turning left at the junction to continue downhill. Above the Grünausee Lake, follow the trail to the right, descending a very obvious moraine ridge. Upon reaching the valley, cross over the footbridge and then ascend toward the turnoff for "Aussichtsbankl Übergschritt" (a detour to a scenic overlook that only take a few minutes). From here, it's a short descent to the Sulzenau Hut.
Alternate route over the Mairspitze summit 2,775 m.: At the junction after the Nurnberger Hut where the main route turns left, take the right trail instead. Ascend this to the pass below the summit of the Mairspitze, and take the trail to the right up to the summit. Return to the pass, and continue over the pass, descending a cabled section. From here, continue to descend, passing the Grünausee Lake until meeting the main route that came over the Niederl. This alternate adds 1 km. and 155 m. of ascent to your day.