I have claimed the 'American Opportunity Credit' and 'Education Credit' for the last four tax years: 2016, 2017, 2018, and 2019. 

OK - THEN IF HE IS A DEPENDENT (SEE THE DEPENDENT QUALIFICATION RULES), THEN YOU OBVIOUSLY CAN'T CLAIM THE AOTC FOR 2020.

These credits were for my son/dependent. 

He graduated in June of 2020, started working; and I will not claim him as a dependent in 2020. 

AND....HE MADE HOW MUCH IN 2020? YOU LEFT OUT AN IMPORTANT FACTOR IN YOUR QUESTION - I NEED TO KNOW THAT IN ORDER TO DETERMINE WHETHER HE IS YOUR DEPENDENT FOR 2020.

I paid $11,503 for his tuition in 2020 (last semester of his senior year). 

I understand the 'American Opportunity Credit' is not available, as if is for only four years. 

BINGO

What about the 'Education Credit'? 

DEPENDS ON WHETHER HE IS A DEPENDENT. YOU'RE ASKING THE QUESTION WITHOUT FIRST KNOWING WHETHER HE QUALIFIES AS A DEPENDENT FIRST

Can I claim the 'Education Credit' on my tax return for 2020 (even though the student, my son, won't be a dependent on my 2020 tax return)? 

OH OK, IF HE IS IN FACT NOT A DEPENDENT OF YOURS, THEN OF COURSE YOU CAN'T CLAIM THE EDUCATION TAX CREDIT. IF THAT WERE TRUE, I'D LOVE TO CLAIM THE EDUCATION TAX CREDIT FOR MY NEPHEW WHO IS NOT MY DEPENDENT!

If I cannot can my son claim an 'Education Credit' for the tuition payment?  (Perhaps, under the concept that this is a gift to my son, which was then used to pay for tuition?)

YEP

Thank you all, in advance, for your thoughts.