The possible existence of the bound states of the interacting two-dimensional (2D) magnetoexcitons with in-plane opposite wave vectors, as well as with antiparallel electric dipole moments oriented perpendicularly to the corresponding wave vectors was investigated in the lowest Landau levels approximation. Two definite spin structures of the two electrons and of the two holes forming the molecule were taken into account. One of them is the singlet-singlet structure in which the spins of two electrons and the effective spins of two holes separately form singlet states. Another one is the triplet-triplet structure. The variational wave functions describing the relative motion of two magnetoexcitons in the frame of the molecule depend on the modulus k in the forms of the ring and of the bell in momentum representation. It was shown that in four spinorbital variants the bound states of the 2D bimagnetoexciton in the lowest Landau levels approximation do not exist. Instead of them in the ring configuration and triplet-triplet spin structure a metastable bound state with an activation barrier comparable with the double ionization potential of the magnetoexciton was revealed. The role of the dipole-dipole interaction in the formation of the bound states is discussed.