When your repository is becoming too big and you using git sparse checkout is not what you want because you just want to get rid of some folders but still want to keep the commit history, then you need to do the following :

for example, you have the following folder structure in Repo_A:

https://someserver/Repo_A.git -> src -> documentation -> src-feature1

you want to put src-feature1 in another new git repo : Repo_B

1 . clone the original repository

git clone https://someserver/Repo_A.git

2 . change current directory to Repo_A

cd Repo_A

3 . filter branch (the branch name here is master)

git filter-branch --prune-empty --subdirectory-filter src-feature1  master 

4 . change your origin url

git remote set-url origin https://someserver/Repo_B.git

5 . push to the new origin

git push origin master

You have now two repo:

https://someserver/Repo_A.git -> src -> documentation -> src-feature1

and

https://someserver/Repo_B.git -> src-feature1

you can delete src-feature1 from Repo_A