serverless-offline: Custom authorizer will not work if http_proxy is specified - aws-api-gateway

Question

I want to use serverless-offline to authenticate with a custom authorizer.
The file serverless.yml is shown below.
functions:
auth:
handler: src/authorizer.handler
...
custom:
serverless-offline:
httpPort: 4000
resourceRoutes: true
...
resources:
Resources:
ProxyResource:
Type: AWS::ApiGateway::Resource
Properties:
ParentId:
Fn::GetAtt:
- ApiGatewayRestApi
- RootResourceId
PathPart: protected
RestApiId:
Ref: ApiGatewayRestApi
ProxyPathResource:
Type: AWS::ApiGateway::Resource
Properties:
ParentId:
Ref: ProxyResource
PathPart: "{proxy+}"
RestApiId:
Ref: ApiGatewayRestApi
ProxyPathMethod:
Type: AWS::ApiGateway::Method
Properties:
AuthorizationType: "CUSTOM"
AuthorizerId:
Ref: AuthApiGatewayAuthorizer
ResourceId:
Ref: ProxyPathResource
RestApiId:
Ref: ApiGatewayRestApi
HttpMethod: ANY
RequestParameters:
method.request.path.proxy: false
MethodResponses:
- StatusCode: 200
- StatusCode: 401
Integration:
IntegrationHttpMethod: ANY
Type: HTTP_PROXY
Uri: https://my-json-server.typicode.com/{proxy}
RequestParameters:
integration.request.path.proxy: method.request.path.proxy
IntegrationResponses:
- StatusCode: 200
- StatusCode: 401
Run it.
$ sls offline
...
offline: ANY /development/auth-test/{proxy*} -> https://my-json-server.typicode.com/{proxy}
offline: [HTTP] server ready: http://localhost:4000 🚀
After that, accessing the following uri will return a normal response.
The custom authorizer does not seem to be working.
$ curl 'http://localhost:4000/development/protected/typicode/demo/profile'
{"name": "typicode"}
Running curl through the api-gateway will result in 401
$ sls deploy
$ curl 'https://xxxx.execute-api.{region}.amazonaws.com/development/protected/typicode/demo/profile' // This is a 401
$ curl 'https://xxxx.execute-api.{region}.amazonaws.com/development/protected/typicode/demo/profile' --header 'Authorization: Bearer {valid_token}' // This is 200
Does serverless-offline go through authentication with http_proxy?
Pardon my broken English!