Statute of Frauds Question?

If person A enters into an oral agreement with person B in which person A promised to care for person B for the rest of person B's life. And in return, person B promised to leave upon his death all his real estate to person A. Person B died several years later leaving a will whereby he gave all his real estate to person C and appointed person C executor. Person A had fully performed his part of the agreement and, upon learning the above facts, sued person C for the real estate. Can statute of frauds be used as a defense? If person A doesn't get the real estate will there be any remedy? Thanks.