Hi Mehnihma,
I test it in my Office 365 account. I am able to create an Inbox rule for Shared Mailbox in Office 365 OWA.
Given this situation, I suggest you follow the steps below to troubleshoot this issue:
1. Reset IE to the default settings.
2. Clear all cached files.
3. Open OWA in InPrivate Mode.
Meanwhile, you are able to create an Inbox rule for a shared mailbox in Outlook 2010 after adding a shared mailbox in Outlook.
Here are the steps to add a shared mailbox in Outlook:
File>Account settings>Account settings>Change>More Settings>Advanced>Add
For more detailed information "Manage email messages by using rules", please refer to the link below:
http://office.microsoft.com/en-us/outlook-help/manage-email-messages-by-using-rules-HA010355682.aspx
Thanks,
Edward Qu