In instances like this where A) the customer has no email server, and B) their "normal" email provider is unwilling/unable to relay email, there are two solutions...
1) Go to their ISP like Comcast, Midcontinent, CenturyLink, or whoever, and get a standard email account. Most will allow relay of SMTP if it's from their own customers if the connection is from within their own ISP network. Most ISP's will give you 5-10 email accounts for free on a business account.
or 2) Download a MSL release from Mitel Online, either standard or virtual, and deploy it at the customer site, and do NOT license it. It is a full blown email server itself. Give it a static IP address and allow email injections from trusted networks, very basic config is all that is needed and no AMC connection. I have even used an old Windows Vista PC the customer had and dropped MSL8 on it (which will run on most hardware, doesn't need to be a server). Word of warning though, if your customer is "cheating" and using a residential Internet connection, this could cause them to get red flagged by their ISP and require them to upgrade to a business account.
Both work, depending on your situation. You can also use a standard Gmail account, I haven't done it personally, but a few techs have mentioned they have used this method on the 5000.