The deposit can stay where it is: you just need to have access to it as the landlord. If you don’t, ask the agency to give you access. You may have to change the ‘landlord’ address details from that of the agency and copy the updated ‘Prescribed Information’ to the tenant.
Anyone can do the future inventory and exit checks, an OpenRent or other contractor. You do need to get the existing one from the agent if you don’t already have it, for use when the tenant leaves.
Finally, check your agency contract: all three that I went to basically had terms that stated they would continue to be paid forever, and in one case, even if I found the next tenant, hence why I am not using an agent, as well as being horrified at the charges they place on both the tenant and the landlord, when some are just cowboys, not professionals.
Hi Thomas, @John45’s answer includes everything I would have said!
If you are able to stop paying the agent, then getting the deposit transfered to you will be easy, because if they don’t do it, then they will still be liable to follow the rules of the deposit return at the end of the tenancy, which they will not want to do ‘for free’.
As long as an inventory is signed by all parties, then it doesn’t matter who performed it