Go to Manage → Integrations → Moneybird → click Connect account. Log into Moneybird and authorize Senly. From now on, invoices you create in Senly are pushed directly to Moneybird as well, with the correct client relation, VAT rates and invoice lines.
Payments received in Moneybird sync back to Senly every 30 minutes. So you don't have to keep track of anything twice.