How to get the custom post list to admin user edit page?

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Here are some steps that may help you:

  1. Use show_user_profile action to insert a form in User edit page:
  2. Use get_post_types function to get a list of registered posts in above form.
  3. Finally use edit_user_profile_update action to save your data.

Here is an example which shows how to add custom fields to user edit page.