Three candidate events of the neutron-rich hypernucleus 6{Lambda}H were uniquely identified in the FINUDA experiment at DA{Phi}NE, Frascati, by observing {pi}+ mesons from the (K-stop,{pi}+) production reaction on 6Li targets, in coincidence with {pi}-mesons from 6{Lambda}H rightarrow 6He+{pi}- weak decay. Details of the experiment and the analysis of its data are reported, leading to an estimate of (2.9pm2.0)cdot10-6/K- stop for the 6{Lambda}H production rate times the two-body {pi}- weak decay branching ratio. The 6{Lambda}H binding energy with respect to 5H + {Lambda} was determined jointly from production and decay to be B{Lambda} = (4.0 pm 1.1) MeV, assuming that 5H is unbound with respect to 3H + 2n by 1.7 MeV. The binding energy determined from production is higher, in each one of the three events, than that determined from decay, with a difference of (0.98 pm 0.74) MeV here assigned to the 0+g.s. rightarrow 1+ excitation. The consequences of this assignment to {Lambda} hypernuclear dynamics are briefly discussed.
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