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We explore the prospects for Twinkle to determine the atmospheric composition of the nearby terrestrial-like planet LTT 1445 Ab, including the possibility of detecting the potential biosignature ammonia (NH3). At a distance of 6.9 pc, this system is the second closest known transiting system and will be observed through transmission spectroscopy with the upcoming Twinkle mission. Although LTT 1445 Ab has been suggested to be a candidate for a Hycean world, constraints on the interior composition based on its mass and radius suggests that the planet lacks a substantial water layer, and thus the proposed Hycean scenario is disfavoured. We use PETITRADTRANS and a Twinkle simulator to simulate transmission spectra for the more likely scenario of a cold Haber world for which NH3 is considered to be a biosignature. We study the detectability under different scenarios: varying hydrogen fraction, concentration of ammonia, and cloud coverage. We find that ammonia can be detected at an ∼3σ level for optimal (non-cloudy) conditions with 25 transits and a volume mixing ration of 4.0 ppm of NH3. We provide examples of retrieval analysis to constrain potential NH3 and H2O in the atmosphere. Our study illustrates the potential of Twinkle to characterize atmospheres of potentially habitable exoplanets. [ABSTRACT FROM AUTHOR]