You can use a bulk operation in order to move (and as such add) all issues from one project into the other one. Basically, go to the issue navigator, select all issues from your source project (Project = <your source project>), then select Bulk Change and move them to the other project.
There are a few things to consider before you start, though:
Both your source and target projects have configuration schemes behind them:
Definitely compare the configurations of your projects and check whether everything you need in your target project is actually there. Add the components and versions you might be missing in the target project. Check if all custom fields you have in your source project are also available in the target project.
Should there be differences in terms of issue types and workflows, consider what you want to achieve. You can add the issue types and workflows of your source project to the target project, or you can decide to migrate issue types and statuses from your target project into other issue types and statuses in your source project. JIRA will present you with a wizard to make the mappings of your choice during the bulk move process. It is important that you have figured out the mapping rules you want to apply beforehand, so you don't get taken by surprise when you are in the middle of the actual move.
Finally, each project has its own project key, which is always the first part of the issue key, the unique identifier of each JIRA issue. Be prepared that the issues you are moving from the source project will get a new issue key in the target project, prefixed with the project key of this target project. JIRA will store the old issue key with the moved issue, so in searches you will still be able to find the issue based on the old key. But the new key - as said - will be different.
Hope this helps!
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