I think, he will get the whole story told by Skyler after the show had ended.
When Walt visited Skyler in the last episode, he was watched by the police, etc. and he had to fight against Jack and his men! Walt cannot risk at that point to be found.
Walt Jr. has proven himself to be not trustworthy to keep a secret this big. In order to convince him about the truth about Hank, someone must tell him that Walt was here to tell his. When Walt phones Walt Jr. in S05E15, Walt Jr. was screaming around in the school, etc. He knows that if he or Skyler told Walt Jr. about Hank, his plan could not work. For example, if they would only go to the police, Jack and his men would probably get revenge on Walt's family, or they would be prepared of seeing Walt.
Skyler seems to have trust in Walt (e.g., she was not telling that he was there), so she let him do his work. After the series ended, she would get called to the Nazi clubhouse and can also see that Todd and the others who threaten her were dead. Plus, she can trade the coordinates of Hank's "grave". At that point, the old story about Walt does not make that much sense and Walt Jr. is maybe willing to hear (and accept) the truth.