The answer is no. The subject of くれる always has to be a giver, and its receiver is generally the speaker. On the other hand, the subject of もらう should be a receiver. I know these differences confuse you because Japanese often skips a sentence subject. In the examples below, the first phrases are all the sentence subjects.
わたしは、かのじょに お金をあげる : legit // わたし=giver : かのじょ=receiver
かのじょは、わたしに お金をあげる : not legit
かのじょは、わたしに お金をくれる : legit // かのじょ=giver : わたし=receiver
わたしは、かのじょに、お金をくれる : not legit.
わたしは、かのじょから お金をもらう : legit. // かのじょ=giver : わたし=receiver
かのじょは、わたしから お金をもらう : legit. // わたし=giver : かのじょ=receiver