Photios, Lexikon s.v. Φοινικήια γράμματα Ν.
“The Lydians and Ionans [report] that letters came from Phoinix the son of Agênor who invented them. But the Cretans report differently that they were developed from writing on the leaves of palm trees [phoinikes].
Skamôn, in the second book of his Inventions, says that they were named for Aktaion’s daughter Phoinikê. The story goes that he had no male children, but that he had daughters Aglauros, Ersê, and Pandrosos. Phoinikê died still a virgin. For this reason, Aktaion named the letters “Phoenician” for her, because he wished to give some honor to his daughter.”
Λυδοὶ καὶ ῎Ιωνες τὰ γράμματα ἀπὸ Φοίνικος τοῦ ᾽Λγήνορος τοῦ εὑρόντος· τούτοις δὲ ἀντιλέγουσι Κρῆτες, ὡς εὑρέθη ἀπὸ τοῦ γράφειν ἐν φοινίκων πετάλοις. Σκάμων δ᾽ ἐν τῆι δευτέραι τῶν Εὑρημάτων ἀπὸ Φοινίκης τῆς ᾽Ακταίωνος ὀνομασθῆναι. μυθεύεται δὲ οὗτος ἀρσένων μὲν παίδων ἄπαις, γενέσθαι δὲ αὐτῶι θυγατέρας ῎Αγλαυρον, ῎Ερσην, Πάνδροσον· τὴν δὲ Φοινίκην ἔτι παρθένον οὖσαν τελευτῆσαι· διὸ καὶ Φοινικήια τὰ γράμματα τὸν ᾽Ακταίωνα, βουλόμενόν τινος τιμῆς ἀπονεῖμαι τῆι θυγατρί.
Suda, s.v grammata
“Letters: Know that Phoenicians were the first to invent letters. For this reason, letters are also called Phoinikeia. People also say that Kadmos first brought them to Greece. And Apis, the Egyptian, brought medicine. Asklepios improved the art itself. Look also in the entry on Phoenician Letters.” [reference is the same as reported in Photios’ Lexicon.]
Γράμματα: ὅτι τὰ γράμματα Φοίνικες ἐφεῦρον πρῶτοι. ἔνθεν καὶ Φοινίκεια ἐκλήθησαν. καὶ τὸν Κάδμον φασὶ πρῶτον ἐς τὴν ῾Ελλάδα κομίσαι· ἰατρικὴν δὲ ὁ ῎Απις ὁ Αἰγύπτιος· ὁ δὲ ᾿Ασκληπιὸς ηὔξησε τὴν τέχνην. καὶ ζήτει ἐν τῷ Φοινικήϊα γράμματα.