Catalyzes the post-translational modification of target proteins by phosphopantetheine. Can transfer the 4'-phosphopantetheine moiety from coenzyme A, regardless of whether the CoA is presented in the free thiol form or as an acetyl thioester, to a serine residue of a broad range of acceptors including the acyl carrier domain of FASN. {ECO:0000269|PubMed:11286508, ECO:0000269|PubMed:12815048, ECO:0000269|PubMed:18022563, ECO:0000269|PubMed:19933275, ECO:0000269|PubMed:21238436}. This is the function of AASDHPPT (aminoadipate-semialdehyde dehydrogenase-phosphopantetheinyl transferase, Ensembl gene identifier ENSG00000149313).