According to a new resolution of the Cabinet of Ministers of Ukraine, Ukrainian men who are abroad have less than a week to register for military service at Ukrainian embassies or consulates.
According to this document, they are obliged to do this within 30 days from the date of entry into force of the Resolution of the Cabinet of Ministers of Ukraine dated May 16, 2024 under number 563.
This resolution enters into force simultaneously with Law No. 3633-IX, which in turn entered into force on May 18.
That is, you need to register by June 17.
Only those men who officially withdrew from military service before leaving Ukraine can do this abroad. And this is an overwhelming minority.
The remaining Ukrainian men living abroad will need to return to Ukraine in order to fulfill the requirement to register for military service. But it is unlikely that there will be many such cases.

