Thank you "analogcd" for your reply.

I did the job nicely and now the new HDD works fine. I just want to mention something for the people that will do the same procedure and might be surprised. After cloning the old HDD and restarting the computer for testing I noticed that, when hitting spotlight, the Mac was indexing the new HDD. This procedure lasted about three hours! I am not into the computer technology so I decided to let it finish first and then test the bootable ability of the new hard drive. Everything went fine as I mentioned above.

Thanks again.