My client's email server is managed externally by another organisation they are affiliated with. The server is Exchange 2010 and my client uses' the other orgs domain name for its own email addresses. The other org only offers tiny inboxes and my client must frequentlly create PST files to ensure their Ex2010 inbox does not get full. These PSTs are kept on my client's Windows server.
My client has Office 365 Business subscription for the 2016 apps. I want to stop the use of PSTs and store the exported email in Office 365 somehow.
I looked at the "Exchange Online Archiving for Exchange Server" Office 365 product but that requires access to the other organisations Windows network to setup AD Conenct and hybrid exchange.
What's the next best solution i can offer my client where the exported email is stored in an Office 365 inbox please?
There's not a lot of elegant options in the environment you describe. Do the Office 365 licenses your client purchased include Exchange Online mailboxes? Perhaps you could add these mailboxes to their Outlook profile and manully drag and drop mail from the hosted mailbox to the Exchange Online mailbox.
Currently they only have O365 Business sub, but I could add an Exchange inbox to each user who needs to archive PSTs. Then add that account to Outlook on their computers. But yes, not very elegant but I suppose it would work.