Look for a repeatable piece of work
The best starting point is often a task that happens regularly and has a recognisable beginning and end. It might be following up outstanding quotes, collecting completion documents or preparing a weekly report. You do not need to hand over everything that a department does.
List what starts the work, what information is needed and what a finished task looks like. If those answers are unclear, spend time making the process visible before handing it over.
Keep decisions with the right people
A workflow can be delegated without delegating every decision around it. Someone can check whether a quote has received a response while your sales team keeps pricing and negotiation. Someone can collect job documents while your service manager keeps technical and safety decisions.
Write down the exceptions that need an approver. The person doing the recurring work should know when to continue, when to ask and whom to contact.
Agree what you will review
Choose useful review points: whether records are complete, whether unresolved items have a next action and whether escalations reach the right person. Review the actual source information rather than relying on an impression that things feel busier or quieter.
A first workflow gives both teams something concrete to learn from. Expand only when the process, quality checks and responsibilities are working as intended.