Fujitsu LIFEBOOK AH512 supported in maximum of 16 GB, 2 Memory slot(s) of RAM. As in technical detail specified that DDR3 1600 MHz will be clocked with 1333 MHz in combination with 2nd generation Intel® CPU
So, The Komputerbay 16GB 2x 8GB DDR3 PC3-12800 1600MHz SODIMM 204-Pin Laptop Memory CL10 is compatible with your laptop.