I believe that the "Definition of Done" is created by the Team and the "Acceptance Criteria" is created by the Customer. Am I correct?
Can a customer define the Definition of Done to the agile team?
Yes, The Definition of Done is created by the Scrum team.
The Acceptance Criteria is created by the Product Owner.
They are orthogonal concepts, but both need to be satisfied to finish a story.
I don't think it is quite as cut and dry as in smp7d's answer.
The Definition of Done is created by the team, but may require the Scrum Master to enforce quality constraints if the team don't have clear development standards. For example, a team may not want code reviews or unit tests, but a Scrum Master may need to enforce them to ensure quality is maintained. In the ideal situation the team see the benefits and want such quality constraints, but the real world isn't always ideal.
The acceptance criteria should be created by everyone but confirmed with the Product Owner. For example the customer or PO may want the ability to log in, but the team add the acceptance criteria of security, performance etc. Just like creating stories, everyone can come up with ideas but the Product Owner has the final say.
Some of these things may overlap. For example in our team rather than specifying acceptance criteria around performance in every story we have moved it into the Definition of Done. A Definition of Done shouldn't be specific to a feature or story but should span at least a project, if not all development.
https://www.scrumguides.org/scrum-guide.html#artifact-transparency-done clearly states that the DoD is defined by the development team.
If "Done" for an increment is not a convention of the development organization, the Development Team of the Scrum Team must define a definition of "Done" appropriate for the product. If there are multiple Scrum Teams working on the system or product release, the Development Teams on all the Scrum Teams must mutually define the definition of "Done".
The Scrum Guide does state:
the Development Team of the Scrum Team must define a definition of "Done" appropriate for the product
which means in the absence of a Definition of Done (DoD), it's on the Development Team to define one. However, IMHO, you can't ignore the "if" that precedes this statement:
If "Done" for an increment is not a convention of the development organization, the Development Team of the Scrum Team must define a definition of "Done" appropriate for the product.
I interpret this to mean that some or all aspects of the DoD may be imposed on the Development Team of the Scrum Team. For example, a defense contractor wins a bid to develop a software application for a U.S. Federal Government organization and the Government organization mandates code review for all software development projects in its portfolio.
In practice, we hope that the Product Owner (probably a Government employee) and defense contractor's Development Team will collaborate to reach a mutually-agreeable DoD. But, it may be that a well-developed DoD is imposed on the Development Team by the Government through the Product Owner.