We investigate here the quasiordering <= of finite sets of finite strings over an infinite set of symbols S. We set K<=L iff it is possible to rename symbols occurring in the strings of L so that any string of K is a subsequence of a string of the renamed L. We prove that <= is a wqo which answers the question raised by J. Gustedt in [GU]. We prove also a stronger version with injective correspondence between strings.

Remark:

[GU]=J. Gustedt, Algorithmic aspects of ordered structures, Ph.D. thesis, Technische Universitaet Berlin 1992.
See also J. Gustedt, Well quasi ordering finite posets and formal languages, J. Comb. Theory, Ser. B 65 (1995), 111-124.