Presidential line of succession...and a former president?

So the line of succession, should a sitting president become incapacitated goes as follows: VP, Speaker of the House, President Pro Temp of the Senate, Secretaries of State, Treasury, Defense, Attorney General, Secretaries of Interior, Agriculture, Commerce, Labor, Health and Human Services, Housing, Transportation, Energy, Education, Veterans Affairs and Homeland Security. Question is, can a former 2 term president of the United States hold any of these positions? Since any of these positions are, technically, a spot in which it is possible to be given the presidency and since nobody can hold office of the presidency for more than two terms. Obviously it's highly unlikely that a former president would ever be nominated for one of these positions and equally if not more so unlikely that everyone in the line of succession would be incapacitated. Just curious if hypothetically it would be allowed.

yes, a former president can. The 22nd amendment prevents someone from being elected a third time, and in some cases a second time. But no one is prevented from succeeding to the presidency.

EDIT: The 25th amendment covers succession, but likewise does not prevent any former presidents from becoming president again.

That person would just be skipped over. I'm not sure if the same is the case for a foreign born person, or the age limit rule.