[en] Microscopic theory of the structure of four-particle hypernuclei and of the reaction _Λ⁴H →π^-+⁴He is developed making use of the hyperspherical functions method in impulse representation. A scheme is presented for building symmetrized hyperspherical functions of systems which involve three identical particles and one particle with a different mass. It is shown that rather smooth potentials of ΛN and NN interactions provide good convergence in the number of included harmonics for both the binding energy and lifetime of the hypernucleus. A satisfactory agreement with the available data is demonstrated for the above properties of four-particle hypernuclei