No single archive saves every board. For example, "Not Safe For Work" (NSFW) boards like /b/ are rarely archived by these services due to the sheer volume of spam and legal risks.
Many archives permit searching by image hash to find where an image was posted. Thread/Post Tracking: 4chan archives list
: One of the most stable archives, specialized in high-traffic boards like /pol/ (Politically Incorrect), /v/ (Video Games), and /tv/ (Television & Film). No single archive saves every board