、。
She wrote him a heartfelt letter, thanking him for his help.
Literal
She [topic-は] him [to-に] friendliness [object-を] put-into letter [object-を] write-and, his [genitive-の] aid [to-に] thanked.
Two clauses linked by 連用形 (stem-form) clause linking — 書き instead of 書いて gives a slightly more written/formal register. 親しみを込めた is a 連体修飾 phrase ('a letter into which she put friendliness') — 親しみ ('friendliness, affection') is the noun form of 親しむ ('be familiar/friendly with'), and 込める ('put into, infuse') is widely used for emotion-into-action constructions (心を込める, 真心を込める).