ーI fed a stray cat that was sleeping in our backyard this morning, and I think he is here to stay.
「今朝裏庭で寝ていた野良猫に餌をあげたら、ここに居着いたようだ」
to feed で「餌をあげる」
a stray cat で「野良猫」
I think he is here to stay. で「彼(猫)が居着いたようだ」
ーI saw a cat sleeping in our backyard and gave him some food. I think he has decided to live here.
「裏庭で猫が寝ているのを見たので、餌をやったら、ここに居着いてしまった」
to give ... some food で「…に餌をあげる」
I think he has decided to live here. で「ここに住むことにしたようだ」
ご参考まで!