The "fossil git export" command can be used to mirror a Fossil repository to Git. (Setup instructions and an example.) But the export to Git is not perfect. Some information is lost during export due to limitations in Git. This page describes what content of Fossil is not included in an export to Git.
Git only supports version control. The additional features of Fossil such as Wiki, Tickets, Technotes, and the Forum are not supported in Git, so those features are not included in an export.
Third-party Git based tooling may add some of these features (e.g. GitHub, GitLab) but because their data are not stored in the Git repository, there is no single destination for Fossil to convert its equivalent data to. For instance, Fossil tickets do not become GitHub issues, because that is a proprietary feature of GitHub separate from Git proper, stored outside the repository on the GitHub servers.
You can also see the problem in its inverse case: you do not get a copy of your GitHub issues when cloning the Git repository. You do get the Fossil tickets, wiki, forum posts, etc. when cloning a remote Fossil repo.
The Git client supports cherrypick merges but does not record the cherrypick parent(s).
Fossil tracks cherrypick merges in its repository and displays cherrypicks in its timeline. (As an example, the dashed lines here are cherrypicks.) Because Git does not have a way to represent this same information in its repository, the history of Fossil cherrypicks cannot be exported to Git, only their direct effects on the managed file data.
Git has only limited support for named branches. Git identifies the head check-in of each branch. Depending on the check-in graph topology, this is sufficient to infer the branch for many historical check-ins as well. However, complex histories with lots of cross-merging can lead to ambiguities. Fossil keeps track of historical branch names unambiguously, but the extra details about branch names that Fossil keeps at hand cannot be exported to Git.
Git requires tags to be unique: each tag must refer to exactly one check-in. Fossil does not have this restriction, and so it is common in Fossil to tag multiple check-ins with the same name. For example, it is common in Fossil to tag each check-in creating a release both with a unique version tag and a common tag like "release" so that all historical releases can be found at once. (Example.)
Git does not allow this. The "release" tag must refer to just one check-in. The work-around is that the non-unique tag in the Git export is made to refer to only the most recent check-in with that tag.
This is why the "release" tag view in the GitHub mirror of this repository shows only the latest release version; contrast the prior example. Both URLs are asking the repository the same question, but because of Git's relatively impoverished data model, it cannot give the same answer that Fossil does.
Check-ins are immutable in both Fossil and Git. However, Fossil has a mechanism by which tags can be added to its repository to provide after-the-fact corrections to prior check-ins.
For example, tags can be added to check-ins that correct typos in the check-in comment. The original check-in is immutable and so the original comment is preserved in addition to the correction. But software that displays the check-ins knows to look for the comment-change tag and if present displays the corrected comment rather than the original. (Example changing the typo "os" into "so".)
Git has no mechanism for providing corrections or clarifications to historical check-ins.
When exporting from Fossil to Git, the latest corrections to a Fossil check-in are used to generate the corresponding Git check-in. But once the Git check-in has been created, any subsequent corrections are omitted as there is no way to transfer them to Git.