I have made up a sentence below.
(1a) He was weak and throughout his adult life suffered from many illnesses.
My friends think I need "he" after "life".
(1b) He was weak and throughout his adult life he suffered from many illnesses.
Do I need "he" there? Thanks a lot.
Both (1a) and (1b) are correct. You can add "he" after "life" or not. It's your choice. The sentence is correct either way. Sentence (1a) has one independent clause, and (1b) has two. Sentence (1a) is the following sentence with the "throughout"-phrase re-positioned:
(1a') He was weak and suffered from many illnesses throughout his adult life.
As you can see, "throughout his adult life" is adverbial modifying the verb phrase "suffered from many illnesses." It modifies that verb phrase whether or not it has a separate subject from the subject of "was weak." Tell your friends that verb phrases can be coordinated: "He [was weak] and [suffered from many illnesses]."