@JoanSerr we had a similar situation with a client recently. I asked my primary contact, the controller, to coordinate a sit down with him, us, and the IT team, so we could work out how we were to communicate, how we would work together, and who would hold responsibilities for what components.
To my pleasant surprise, the owner of the company also attended the meeting and opened with a statement of understanding (paraphrased): ""Weather I pay you (the IT firm) or you (the software consulting firm), doesn't matter to me. If I have down time because the two of you can't agree on who is responsible, that does matter to me; a lot! If we have a issue, you both have a issue until the issue is resolved.""
After that, things work much more smoothly. If they need to do something to any server running one of the apps we support, they call us first. If we need anything adjusted on a server or workstation, we don't do it, even if we have the ability. We called them, explain what we need and why, and they make it happen. If we have a disagreement, we discuss it, present the opposing concerns to management, and they direct us on which approach to take.
Life is good. - Don't operate in a vacuum, especially when it's not your risk! Get the client involved. They write the checks and can apply pressure where it is needed.