  This note is a response to one of the problems posed by Kwa\'sniewski in
[1,2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic
sequence $F$ is at the point product of primary GCD-morphic sequences and any
GCD-morphic sequence is encoded by natural number valued sequence satisfying
condition (C1). The problem of general importance - for example in number
theory was formulated in [1,2] while investigating a new class of DAG's and
their correspondent p.o. sets encoded uniquely by sequences with
combinatorially interpretable properties.
