Is there any solution using Azure pipeline to automatic push in the second repository or any other solution?
There is no directly settings you could do that, but you could create a pipeline to invoke the git command to sync the single file between 2 different repositories.
Create a pipeline for the Repo A with trigger settings:

Then add inline powershell task:
cd $(Agent.BuildDirectory)
git clone https://PAT-HERE@dev.azure.com/{organzition}/{project}/_git/{repo-name}
cd {repo-name}
git checkout branch-name # if the synced file not in master
# Assuming the synced file name is "test.txt" and he exists in the folder "common"
Copy-Item $(Build.SourcesDirectory)\_fileS $(Agnet.BuildDirectory)\{repo-name} -Force
git config --globa user.email "xxxx.com"
git config --global user.name "xxxxx"
git add common/_fileS
git commit -m "Sync _fileS"
git push