V. Gregori and S. Romaguera  obtained an example of a fuzzy metric space (in the sense of A. George and P. Veeramani)
that is not completable, i.e. it is not isometric to a dense subspace of any complete fuzzy metric space; therefore, and contrary
to the classical case, there exist quiet fuzzy quasi-metric spaces that are not bicompletable neither D-completable, via (quasi-)isometries. In this paper we show that, nevertheless, it is possible to obtain solutions to the
problem of completion of fuzzy quasi-metric spaces by using quasi-uniform isomorphisms instead of (quasi-)isometries. Such
solutions are deduced from a general method, given here, to obtain extension properties of fuzzy quasi-metric spaces from
the corresponding ones of the classical theory of quasi-uniform and quasi-metric spaces.