Both are perfectly correct. I also agree that the second sentence sounds more "comfortable". Now, be careful: this doesn't work for every verb! We can use "he gave her the keys" because "give" needs two objects: the thing that you give, and the person who receives it. So, you need to make sure that the verb you have can actually take two objects.

Both are correct but the first is slightly more formal.

In my experience, and this is by no means scientific evidence, B is more common, more natural.

Both are commonly used and correct.