It's version 0.6.1 I fixed the set command before, if the user didn't exist, it wouldn't record him.

handlers/schedule.py

@@ -81,11 +81,13 @@ def register_handlers(dp: Dispatcher, state: BotState):
             builder.button(text=group, callback_data=f"set_group:{group}")
         builder.adjust(5)  # количество кнопок в строке
 
-        await message.answer(
+        msg = await message.answer(
             "Выбери группу из списка:",
             reply_markup=builder.as_markup()
         )
 
+        save_message(msg.chat.id, msg.message_id)
+
     @dp.callback_query(lambda c: c.data.startswith("set_group:"))
     async def process_group_choice(callback: types.CallbackQuery):
         group = callback.data.split(":")[1]
@@ -94,5 +96,6 @@ def register_handlers(dp: Dispatcher, state: BotState):
         # редактируем сообщение: убираем клавиатуру
         await callback.message.edit_reply_markup(reply_markup=None)
 
-        await callback.message.answer(f"✅ Группа установлена: {group}")
+        msg = await callback.message.answer(f"✅ Группа установлена: {group}")
+        save_message(msg.chat.id, msg.message_id)
         await callback.answer()