How to move GIT repository content to Monorepo repository with preserving commit history and branches?

Question

I'm about to move my Next.js project repository to Turborepo, for visualization this is the folder structure:

root
├── app/
│   └── my-app
├── packages/
│   ├── ui
│   └── hooks
├── node-modules
├── package.json
├── gitignore
├── turbo.json
└── README.md

I have cloned my-app repository from a remote URL, I want to move all commit history and branches into another repository that is located at the root, so when I'll what will be the best approach to achieve this result?