We propose to investigate AgFBF4, a compound known for > 20 years, with muon spectroscopy. The scope is to determine the 3D ordering temperature as well as estimate the value of J for this Ag(2+)-based 1D antiferromagnet, which shows the shortest Ag-F bond length ever measured (~ 2 Å). Our rigorous DFT calculations (both +U and hybrid HSE06) point to an unprecedented large absolute J of 331 meV, which is >30% larger than that measured for Sr2CuO3. The J values are usually reproduced with satisfactory accuracy at this level of calculations, for example the value computed for Sr2CuO3 is -253 meV (= overestimated by < 5%). If this is confirmed by experiment, fluoroargentates(II) would outperform isoelectronic oxocuprates(II) and rank second to none as far as the absolute value of J via one atom is considered. Moreover, AgFBF4 should be even closer to perfect 1D behaviour than Sr2CuO3.