This is false. This would preclude a fromer President from holding a variety of elected offices and offical government positions because the order of succession is very lengthy. And past Presidents have continued in public office and service after they were president.
The Succession Act simply skips ineligible people. For instance, a foreign-born person could well be Speaker of the House, but in the event that the President and Vice President were rendered unable to discharge the duties of the office, the Speaker would simply be skipped and the President pro tempore would be sworn in as President. The reason that Vice President is special is because of the 12th Amendment that specifically forbids anyone ineligible for President from being Vice President.
“The ‘Twenty-second Amendment of the United States Constitution sets a term limit for the President of the United States, providing that “No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once.”
He cannot serve in any office that would lead to the line of succession.
LLS
Also try the 12th Amendment...
“no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.”
LLS