From the underwater photograph and the microscopic ones, it is surely a sponge (phylum Porifera). However, for a more detailed identification you will need to find a specialist, preferably within your geographic area.
if your specimen has microscleres you should make some spicule preparations for both, light microscope and scanning electron microscope. If microscleres are lacking you can try to do species determination based on histological preparations but it will be quite difficult.