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The second generation Extreme Universe Space Observatory on a Super-Pressure Balloon (EUSO-SPB2) mission is a stratospheric balloon mission developed within the Joint Exploratory Missions for Extreme Universe Space Observatory (JEM-EUSO) program. The Fluorescence Telescope (FT) is one of the two separate Schmidt telescopes of EUSO-SPB2, which aims at measuring the fluorescence emission of extensive air showers from cosmic rays above the energy of 1 EeV, looking downwards onto the atmosphere from the float altitude of 33 km. The FT measures photons with a time resolution of 1.05 \\(\\mu\\)s in two different modes: single photon counting (PC) and charge integration (KI). In this paper, we describe the latter and report on the measurements of its characteristics. We also present a new trigger based on this channel, the so-called KI trigger, which allows to measure additional types of events, namely very short and intense light pulses. We report on the tests of this trigger mode in the laboratory and at the TurLab facility, and its implementation in the EUSO-SPB2 mission.