سَلَّمْتُ عَلَى يَشْكُرَ. — I greeted a person named Yashkur.
سَلَّمْتُ: past verb; تُ is its subject.
عَلَى: preposition.
يَشْكُرَ: genitive noun with fatḥa because the expression is a diptote proper name.
In this sentence Yashkur is naming a person, not reporting the action “he thanks.”