Here are two possible solutions:
Either copy repository A into a separate directory in larger project B, or (perhaps better) clone repository A into a subdirectory in project B. Then use git submodule to make this repository a submodule of a repository B.
This is a good solution for loosely-coupled repositories, where development in repository A continues, and the major portion of development is a separate stand-alone development in A. See also SubmoduleSupport and GitSubmoduleTutorial pages on Git Wiki.
You can merge repository A into a subdirectory of a project B using the subtree merge strategy. This is described in Subtree Merging and You by Markus Prinz.
git remote add -f Bproject /path/to/B
git merge -s ours --allow-unrelated-histories --no-commit Bproject/master
git read-tree --prefix=dir-B/ -u Bproject/master
git commit -m "Merge B project as our subdirectory"
git pull -s subtree Bproject master
(Option --allow-unrelated-histories
is needed for Git >= 2.9.0.)
Or you can use git subtree tool (repository on GitHub) by apenwarr (Avery Pennarun), announced for example in his blog post A new alternative to Git submodules: git subtree.
I think in your case (A is to be part of larger project B) the correct solution would be to use subtree merge.