Hi, Jeremy Heath
This sounds less like a normal sharing mistake and more like Loop not completing the invite flow for that specific Microsoft account. Since a different MSA works, I would treat it as an account/session/storage issue first, not as a recipient-side problem.
Here are some suggestions you can try:
First, sign in to https://outlook.com with the Hotmail account, then open Loop again in a private browser window and retry the invite. For personal Microsoft accounts, signing in to Outlook once can set up things Loop needs for that account.
Make sure the workspace is not My workspace. If it is, create a new normal Loop workspace from the Loop home page and try adding members there. Personal “My workspace” areas are not meant to work like shared workspaces.
Try sharing a page instead of adding the person as a workspace member. Open the page, choose Share, and send a page link to the specific person. This is a practical workaround because page sharing does not rely on the workspace member list being updated first.
Check the Hotmail account’s Microsoft storage. Loop for personal accounts counts against Microsoft storage, and storage problems can cause odd behavior across Loop, Outlook, and OneDrive. Empty deleted Loop workspaces/pages and free space in OneDrive or Outlook if the account is near its limit.
If none of that works, contact Microsoft Support and include the comparison test in the support case: “Same browser, same workspace steps, Gmail-based MSA works, Hotmail MSA says added but no member appears and no email is sent.” That makes it easier for support to see this is isolated to the Hotmail identity rather than the workspace itself.
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Thank you for your patience in reading, I hope this information has been helpful to you.
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