I couldn’t find any tutorial videos for the exact variation of the fireman’s carry that we did in BJJ class 162. All the videos I found were either a standing or kneeling variation, while I would describe the one we did as a “sliding, sitting” fireman carry.
This blurry Spanish video is wrestling oriented, but it has the same variation of the throw (the grips might be different) with the sitting and leg-positioning. It’s identified as a sit-down and later as on-knees firemans carry.
And just for good measure, here’s another BJJ variation that I want to show as the video has a great nugget of advice in adapting a technique to a Brazilian Jiu-Jitsu mindset – that is, besides the obvious gems in the actual takedown setup, technique, and submission.