Infinitely many Carmichael numbers in reduced residue classes

Let $M$ be a positive integer, and let $a$ be an integer such that $(a,M)=1$. A Carmichael numbers in arithmetic progressions conjecture. There are infinitely many Carmichael numbers $m$ such that

$$m\equiv a\pmod M.$$

The paper's abstract states that this result is proved, so the conjecture is resolved by the paper itself.