Use gitlab with existing gitrepo-server in production

Actually I am already using gitrepo as client and server based architecture where MachineB is remote GItRepo Server and all the development work is push over MachineB from MachineA.

MachineA= localusers
MachineB= gitrepo-Server
MachineC= gitlab-server

Here I want to use gitlab for the project review and the better visualization which provide me a UI like gitHUb. But I dont want to stop using gitRepo-server which is existing running from a long time and is production repo.

problem is here gitlab has its own git setup and for using gitlab in production with gitRepo-server (machineB) means devlopers needs to push code on two place.

I am looking for a solution by which MachineA whenever push the code to MachineB it automatically reflect over machineC (gitlab server) to minimise time and management afford.

Please provide the inputs. Thanks