How to convince Business Partners in the Agile transformation?

'Convince' would not be the right method. The intent should be to impress upon them the value and link to achieving business goals and better alignment with the organization's strategic goals. Provide enough information for the decision makes to believe that moving in 'this' direction is the right / best thing for the organization.

And, yes, as you mention, engagement (and partnership!) is a great path in which to achieve it.

Agree re valid business case.
Good to explore the details and confirm understanding of: Agile approach, need for Agile in the organisation (if any), benefits of Agile, cost / benefit analysis etc.

I'm not sure about the question. Some background about 'need to convince' would help.

The need to convince has to be a valid business case. The economic-impact-analysis should give some insight about 'what need to be changed' and 'how that change can be implemented'.

The 'agile transformation' do not have same impact/benefits for every organization. There will be many influencing factors.The adoption of business practices to suit partner organization has to be a custom effort with targeted financial impact.