Search engines don't like to index content that is no longer available. Once they discover it is unavailable, search engines will remove the content from their index.
The time frame for removal depends on two factors:
- How often the search engine crawls the page, which is determined largely by how popular the page is.
- What type of HTTP response code the removed content has.
If your post has many links to it from popular websites, it could get crawled several times a day. Most likely that isn't the case. Googlebot returns to re-crawl less popular content every few weeks.
Once Googlebot crawls the removed page, it will schedule it to be deleted from the index. If it finds a "404 Not Found" status, it will give it a 24 hour grace period, and then remove it from the index. If it finds a "410 Gone" status, it will remove it as soon as it can, usually within a couple hours.
I don't know what type of HTTP status Facebook uses for deleted posts. But that probably isn't the limiting factor. The limiting factor is the crawl rate. I would expect your content to be gone from the search engines in 3 to 6 weeks.
If it were you own site on your own domain (not on Facebook) you could log into Google Search Console and speed the crawl process along. You could submit a Fetch as Google request or a URL removal request. However, those requests only work if you control the domain and can verify that ownership as part of the process of signing up for Google Search Console.