A former colleague offers to introduce you at a company in an industry you want to move into. They know your work well. They know much less about the role you're targeting.
Sending your résumé is reasonable. Expecting them to explain the fit from that alone isn't.
I'd prepare a short case before asking for a recommendation. That doesn't mean waiting until you've answered every question. If you still need to understand the work, ask for an exploratory introduction. Don't ask someone to endorse a fit neither of you has established.
An introduction is not an endorsement
An introduction says you two should talk. An endorsement adds a judgment about why you're suited to the work. Keep those commitments separate.
Your colleague might have watched you lead a difficult project and be happy to recommend that ability. That doesn't mean they can assess your knowledge of a different industry. Asking for a broader endorsement puts their name behind a conclusion they may not be equipped to reach.
They can describe what they saw you do and explain why they think it's relevant, while leaving the untested part open. The hiring manager still has to assess you.
Check the work before you polish the pitch
Start with what the employer needs this person to deliver. What prompted the hire? Which decisions must the new manager handle from the start? The job description may not reflect today's priorities, so confirm those with someone who knows the team.
If you can reach someone who has made a similar move, ask where their previous experience helped and what they had to learn. Use that conversation to test your target, not collect reassurance.
Keep two lists: what you've confirmed and what you're assuming. The length of the second list matters less than what's on it. An unknown reporting detail and an unknown day-one requirement aren't the same problem.
Suppose you led a system rollout while a specialist made the technical decisions. That's relevant experience in coordinating delivery. It doesn't establish that you can fill a role whose main purpose is making those technical calls. If that is what the employer needs on arrival, you need a different target or more preparation, not a better introduction.
If the important question is still open, make it the reason for the exploratory conversation. You don't need to solve the company's problems before meeting anyone. You do need to explain what you want to learn.
Write something they can assess and forward
I've hired thousands of people across the globe. When I hire, I listen for whether someone actually did the work they're describing or stood near the person who did. A referral note should give the hiring manager enough substance to begin that assessment.
Write a short note in your own voice. Open with the specific role or business need you're interested in. Then give one relevant example: the situation, your responsibility, the decision you made and the result. Include a timeframe and a measure of the result where you can substantiate them. Name your contribution without claiming the team's work as your own.
The opening explains why you're writing. The example supplies the evidence. A polished description of the kind of leader you are cannot do both jobs.
End with a clear request. For a role you understand and have relevant evidence for, that might be a conversation about joining the interview process. If fit remains uncertain, say what you need to understand, such as whether the employer needs an experienced industry specialist or someone who has led comparable work elsewhere.
Keep confidential figures, customer names and internal documents out unless you have permission to share them. Checkable does not mean attaching your current employer's files.
Let your contact set the limit
Go back to your contact and ask: which parts of this can you stand behind, and what would you need to understand better before you're comfortable sending it?
Ask them to separate what they observed from what they're taking on your word. Their enthusiasm may be genuine. It still isn't proof that you can do the new job.
Keep your note identifiable as your account. Let your colleague add their own explanation of how they know you and what they can recommend. Don't draft praise in their voice or turn permission to forward your note into permission to claim their endorsement.
If they can recommend your relevant work, agree on that narrower claim. If they can only connect you, ask for an exploratory introduction and make its purpose clear to the recipient. If they identify a gap, find out whether they lack information or whether you lack something the role requires. Those lead to different next steps.
If your search is confidential, agree who may receive the note and what may be shared before it goes anywhere. An agreement can't prevent another forward. If that exposure would be unacceptable, keep the discussion private rather than circulating a ready-to-send note.
For a live opening, follow the employer's application process. Don't let a promised introduction hold up other applications or conversations. Not everyone has a willing contact, and a well-made case doesn't create an opening, a capability, or a market.
An unanswered message doesn't explain why someone stayed quiet. They may be busy, lack access or have reservations. Follow up if appropriate, but don't treat silence as proof that your explanation failed. Use specific feedback to improve the case or reconsider the target.
If your colleague can offer an introduction but not an endorsement, don't argue them into one. Use the conversation to find out whether this is the move you should make.
A big interview or an offer on the table?