Who among the following sits exactly between F and A?

Only one person sits between H and A who sits third from the one of the ends of the row. As per this statement, there will be four possible cases and the arrangement will look like this: D sits to the immediate left of H. As per this statement, CASE I will get eliminated and we will continue with CASE I (A), CASE II and CASE II (A) and the arrangement will look like this: F sits third to the left of G. F does not sit at the end of the row. As per this statement, CASE I (A) will get eliminated and we will continue with CASE II and CASE II (A) and the arrangement will look like this: C sits three places away from G. As per this statement, CASE II will get eliminated and we will continue with CASE II (A) and the arrangement will look like this: More than three persons sit between B and A. As per this statement, the final arrangement will look like this: