Sec80gg and sec 10(13a)

Pranams all, My doubt is regarding claim of 80GG if a person is recieving HRA from employer( bear with me), and all other conditions for claiming 80GG are met. Is it possible he could add back the amount of HRA recieved to his salary(total income) without claiming 10(13A) and instead claim HRA under 80GG?? lets imagine this person pays 6000 every month as rent but employer gives HRA of 500. adding 500x12=6000 back to his income and claiming HRA under 80GG is more profitable to him. but can it be done??? Hope you understand my query clearly. Thank you in advance