I want to be able to share answers using anchor links, such that when the link is visited, the page scrolls to the particular answer instead of showing the top of the page.
A good example is seen with this link.
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Just click the 'share' link below the answer. It will do exactly what you want, in the browser but even in the Stack Exchange mobile apps.
For example, this link (
https://meta.stackexchange.com/a/19499/295232) goes directly to the Jon Skeet meme answer, not to the question.
It's not possible to link to a specific place in an answer (or question), see Support anchor names in posts