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So if it is an F, I don't know if anyone here is familiar with stampworld.com but that where I inventory all my stamps. When I go to "1868" stamps for U.S. there is absolutely no option for this stamp. My choice is only the "1867" version. So is it possible the website has misinformation bout the true history or it is in fact a different type grill
"Inventory" and "catalog" are two very different things. We are all familiar with stampworld; it is a useful site for attempting to identify the origin and year of issue for a stamp, and that's about it. It orders stamps chronologically, and doesn't use any catalog numbering system. You can't, for example, go to a dealer and ask them for a MNH copy of Germany stampworld #547, for example.
Since it's ultimately a simple system, it does not go into variants of any kind (paper types, plates, printers, errors, watermarks, etc). To suggest stampworld has "misinformation" about the stamp in a way gives the site too much credit; it doesn't have misinformation about the stamp, because it's not supposed to have that kind of information at all.
The resource(s) you need are actual catalogs, such as Scott, Michel, Yvert, etc.