AWS lambda Python functions gives error to install the "google-cloud-firestore" module, but is already installed

lambda_function と、pip install --target . firebase-admin==5.2.0 および pip install --target . grpcio で生成されたアップロード済みパッケージから始めます。AWS Lambda のインポート失敗を再現し、パッケージの内容とランタイムエラーを調査します。デプロイされた Python 3.9 関数がモジュール不足エラーなしに Cloud Firestore をインポートして使用できれば完了です。

Operating System version: AWS Python lambda
Firebase SDK version: firebase-admin 5.2.0
Firebase Product: google cloud firestore
Python version: 3.9

Hi I have an AWS Lambda in Python 3.9 (now regenerated in AWS functions console),I have installed in my local aws folder firebase-admin & dependencies:

pip install --target . firebase-admin==5.2.0

This installation gives me this error:

And finally I have implemented my Python AWS lambda, and upload to AWS lambda as ZIP file a package to the AWS code function console. When I tried to execute my testing in the Python Lambda, this gives me this error:

{
  "errorMessage": "Unable to import module 'lambda_function': Failed to import the Cloud Firestore library for Python. Make sure to install the \"google-cloud-firestore\" module.",
  "errorType": "Runtime.ImportModuleError",
  "stackTrace": []
}

I also installed in my local directory the grpcio module, before to upload ZIP file in AWS function console, with this command:

pip install --target . grpcio

And finally upload all my directory in a package to the AWS function console.

But the same error is displayed when I execute a test in AWS cloud function.

{
  "errorMessage": "Unable to import module 'lambda_function': Failed to import the Cloud Firestore library for Python. Make sure to install the \"google-cloud-firestore\" module.", ....
}

This is my full directory:

What can I do to solve this error? & made available google-cloud-firestore works fine in my AWS Lambda Python?

Thanks!