Restrict login to Enterprise Google Domain for AWS

I'm using a federation identity pools with aws-amplify (https://aws.github.io/aws-amplify/media/authentication_guide#enabling-federated-identities) and I'd like to restrict the scope of domains to just my google domain organization (ex. johndoe@foobar.com).

There doesn't seem to be a way to lock it down on either the Google API console or the AWS Cognito Identity Pool settings, just a hint that an hd parameter can be appended to the google request to restrict it by domain (which would still require modifying the aws-amplify core package), and it still wouldn't be secure since anyone could just make the same request without the hd and gain access to cognito.

My question is this: is there a way to restrict a google oauth key to only allow @foobar.com email addresses, or to implement the same restriction with aws cognito?

I believe I found a solution (from several quick tests it seems to be working fine)

Don't try to control the hosted domain part via the Trust Relationship in the Role.

Go to: Cognito / Edit Identity Pool / Authentication Providers

Select Google+

In "Authenticated role selection" select "Choose role with Rules"

Now require claim "hd" to be "equals" to <your-domain>

set "Role resolution" to "DENY"

Source: https://forums.aws.amazon.com/thread.jspa?messageID=527303

Here's a cloudformation stack to set everything (identity pool, roles, etc.) in one go. YOU NEED TO MAKE THE NECESSARY ADJUSTMENTS at all places marked with an EDIT HERE: comment.

AWSTemplateFormatVersion : 2010-09-09
Description : "An Identity Pool stack which uses Google for sign-in"


Resources:
  IdentityPool:
    Type: AWS::Cognito::IdentityPool
    Properties:
      IdentityPoolName: identity_pool_a
      AllowUnauthenticatedIdentities: false
      SupportedLoginProviders: 
        # EDIT HERE:
        "accounts.google.com": "11111111111-22222222222222222222222222222222.apps.googleusercontent.com"

  IdentityForbiddenRole:
    Type: AWS::IAM::Role
    Properties:
      MaxSessionDuration: 3600
      AssumeRolePolicyDocument:
        Version: "2012-10-17"
        Statement:
          - Effect: Allow 
            Principal:
              Federated: "cognito-identity.amazonaws.com"
            Action:
              - "sts:AssumeRoleWithWebIdentity"
            Condition:
              StringEquals: 
                "cognito-identity.amazonaws.com:aud": !Ref IdentityPool
              ForAnyValue:StringLike:
                "cognito-identity.amazonaws.com:amr": unauthenticated
      Policies:
        - PolicyName: None
          PolicyDocument:
            Version: "2012-10-17"
            Statement:
              - Effect: Deny
                Action: "*"
                Resource: "*"

  IdentityAllowedRole:
    Type: AWS::IAM::Role
    Properties:
      MaxSessionDuration: 3600
      AssumeRolePolicyDocument:
        Version: "2012-10-17"
        Statement:
          - Effect: Allow
            Principal:
              Federated: "cognito-identity.amazonaws.com"
            Action:
              - "sts:AssumeRoleWithWebIdentity"
            Condition:
              StringEquals: 
                "cognito-identity.amazonaws.com:aud": !Ref IdentityPool
              ForAnyValue:StringLike:
                "cognito-identity.amazonaws.com:amr": authenticated
      Policies:
        - PolicyName: UserPermissions
          PolicyDocument:
            Version: "2012-10-17"
            Statement:
              - Effect: Allow
                # EDIT HERE:
                Action: "s3:GetObject"
                # EDIT HERE:
                Resource: "arn:aws:s3:::my-bucket/*"

  RoleAttachment:
    Type: AWS::Cognito::IdentityPoolRoleAttachment
    Properties:
      IdentityPoolId: !Ref IdentityPool
      Roles: 
        unauthenticated: !GetAtt IdentityForbiddenRole.Arn
        authenticated: !GetAtt IdentityForbiddenRole.Arn
      RoleMappings: 
        accounts.google.com:
          AmbiguousRoleResolution: Deny
          Type: Rules
          RulesConfiguration:
            Rules:
              - Claim: hd
                MatchType: Equals
                # EDIT HERE:
                Value: mydomain.com
                RoleARN: !GetAtt IdentityAllowedRole.Arn