how to handle server downtime for webhook requests in java

My application(A) gets file processing details from another java application(B) through rest api. App B sends the status with real-time processing details (Inprogess, Generated, Transfered). Application reads this info and displays it to the user. when the status is Transfered.. App A performs some task.

App A is completely dependent on App B for performing future task.

Looking for best practise to handle the request from App B during my app A downtime.

I found that message queue is best solution for this usecase. Unfortunately we cant have any new infrastructure for message queue.

Is there any other solution that we can implement in java without having any infra level changes. I appreciate your time for going through this query. Thankyou