Can a vpc Link be used for a HTTP API (Account A) to trigger a private rest api in account B through a VPC endpoint using Cloud Map

Yes, you can use Cloud Map with VPC Links to trigger a private REST API in another AWS account through a VPC endpoint. Cloud Map provides service discovery for your resources, including private endpoints.

Please follow the below steps:

1. Create a service in Cloud Map for your private REST API in Account B. This service will register the private endpoint's DNS name.

2. In Account B, set up a VPC endpoint for API Gateway, which your private REST API is deployed to. This endpoint will enable communication between the HTTP API in Account A and the private REST API in Account B.

3. Create a VPC Link for your HTTP API in Account A. Configure the VPC Link to point to the VPC endpoint DNS name registered with Cloud Map.

4. Now, your HTTP API in Account A can use the VPC Link to communicate with the private REST API in Account B. You can use the endpoint URL provided by API Gateway for the private REST API, or dynamically using the format you mentioned (https://{rest-api-id}-{vpce-id}.execute-api.{region}.amazonaws.com/{stage}).

Also, please make sure you have proper IAM permissions set up to allow the HTTP API in Account A to invoke the private REST API in Account B. Also, ensure that the security groups and route tables are properly configured to allow traffic between the VPCs and the VPC endpoints.