気付 has multiple meanings. When you use as a verb 気付く (kizuku), it means "realize," "notice," and something like that.
The other meaning is derived from word-for-word translation of c/o in English. When it is used for this meaning, you don't add く to it and it is pronounced "kizuke."
So the translation of the ex2 is:
彼の会社気付でこの荷物を送って下さい。(Kare no kaisha kizuke de kono nimotsu wo okutte kudasai)