How to check links?

We agreed with the owner of a similar site to place links to each other on their sites. On April 9, a link to my site was posted on his site. On April 11, the robot visited the site and wrote in the report that there were no external links leading to the site. Why did it happen? Hasn't enough time passed yet or what? Are there any services to speed up the indexing of external links, or maybe there are some effective ways to check the indexing?