It is a bit difficult to give specific assistance without specific information @ahmed-future. If you are just moving a domain from account to another and none of the underlying pointers are changing then it should be smooth? If what email plan they are using changes, if what hosting they are using changes... Then some downtime should be expected.
Depending on what email plan they are on the emails may or may not move with the website. cPanel email as an example would not move without some backup and restore being done. If you are changing nameservers there could be up to 48 hours before changes propagate? It also depends on how your clients currently connect to their email.
Since you have a request for no downtime I'd say backup, backup, then backup all essential information. To have no downtime isn't really possible in my eyes. Usually I would start something like this in the early hours but you can't really ever know if some emails slip into the abyss if you are changing servers. Does that clarify anything?
...turns out that my two cents is worth less or more depending on the current exchange rate.
roy darling *my posts seem a lot shorter in my head