Born-Oppenheimer molecular dynamics simulations have been performed to investigate the proton-transfer mechanism in liquid phosphonic acid at different temperatures. The transfers are observed if additional charge carriers are present. The liquid phosphonic acid has been characterized by pair-distribution functions, self-diffusion coefficients, and hopping rates. Moreover, we find that the proton transfer is prepared by the following necessary local geometrical criteria: (1) an O-H-O angle close to 180 degrees and (2) an O-O distance lower than 2.5 angstrom. However, we observe in many cases a Zundel-like species, in which an excess proton is shared, complexed, and stabilized by two adjacent phosphonic acid molecules. These unsuccessful attempts to transfer a proton fulfill the same local criteria as successful transfers, and thus, we conclude that nonlocal requirements may play an important role for the success of the transfer too.