问题的解决需要在API Gateway的设置中进行配置。具体来说，需要启用“AWS_IAM”身份验证类型，并将API Gateway上的Cognito用户池与相应的作者器ARN（Amazon资源名称）关联起来。 以下是一个Python的代码示例，用于在API Gateway中启用身份验证类型和关联Cognito用户池：

import boto3
import json

client = boto3.client('apigateway')

rest_api_id = 'your_rest_api_id'
resource_id = 'your_resource_id'
method = 'your_http_method'

# Enable AWS_IAM authorization
client.update_method(
    restApiId=rest_api_id,
    resourceId=resource_id,
    httpMethod=method,
    patchOperations=[
        {
            'op': 'add',
            'path': '/authorizationType',
            'value': 'AWS_IAM'
        }
    ]
)

# Associate Cognito User Pool with Authorizer ARN
authorizer_arn = 'your_authorizer_arn'
cognito_user_pool_id = 'your_cognito_user_pool_id'

client.create_authorizer(
    restApiId=rest_api_id,
    name='cognito-authorizer',
    type='COGNITO_USER_POOLS',
    identitySource='method.request.header.Authorization',
    providerArns=[authorizer_arn],
    authType='cognito',
    authorizerUri=f'arn:aws:apigateway:{aws_region}:lambda:path/2015-03-31/functions/{your_lambda_function_ARN}/invocations',
    authorizerResultTtlInSeconds=300,
    authorizerCredentials='arn:aws:iam::{your_account_id}:role/{your_cognito_authorization_role}',
    identityValidationExpression='^[A-Za-z0-9-_=.]+(\.[A-Za-z0-9-_=.]+)*@[A-Za-z0-9-]+(\.[A-Za-z0-9-]+)*(\.[A-Za-z]{2,})$',
    providerARNs=[authorizer_arn],
    cognitoUserPool={
        "poolId": cognito_user_pool_id,
        "awsRegion": aws_region
    }
)

通过这个代码，你可以把Cognito授权信息转发到你的Lambda函数中。