can I not mention that I have will complete a PhD degree while applying for another one in another country
The comment of Jeff is worth considering. Do you really need a second doctorate to migrate.
But, under the circumstances, send a message to the new university stating that since your application, you were awarded a PhD, but, assuming you want to, that you still want to continue your application and enter the new program. Stress that the research proposal will be different if accepted.
Hiding the recent degree could come back to harm you.