Sync allocated task time back to Obsidian

I use Morgen alongside Obsidian, importing tasks via the 🆔 tag on each task line. When I allocate a time slot for a task in Morgen, I'd like that time to be written back into the Obsidian task line (e.g. next to the 🆔), so I can see at a glance what time was scheduled without opening Morgen.

Ideally this would be two-way: if I change the time in Morgen, it updates in Obsidian; if I change it in the Obsidian line, it updates in Morgen. Right now the sync only goes one direction (Obsidian → Morgen), so once a task is scheduled I lose visibility of its time inside the vault.