To help you better, I need more details for better understand your issue.
Main desktop computer is using Microsoft Office Home & Business 2019. ··· A remote employee needs to install Microsoft on their computer.
Do you mean in the same organization, users use different versions of Office. One is Home & Business 2019, the remote employees use other verions? If so, from the general use of Office, there is no conflict between newer versions.
We want to be sure that both computer users may view, edit and save the same documents.
Newer Office can open common Office files, such as .docx, .xlsx, etc.
Besides, if you want to sue 'Document collaboration and co-authoring', that store files on OneDrive or SharePoint, then share this file to employees. You need to meet following conditions to co-author a document.
What might be the best subscription to go with for the laptop computer user?
For organizations, I suggest Microsoft 365 Business subscriptions. You can have more control over how users use Office. Any misunderstandings, please feel free to let me know.
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