You need to set up a separate MAPI profile in Outlook under Jane’s user context for the customer service account and configure Outlook so that it prompts for the profile to open when launched. Jane will also require permission to the customer service mailbox granted in Active Directory. Once this is all configured accordingly, Jane can easily switch between profiles simply by closing Outlook and opening it again and selecting the alternate account.
To prevent from needlessly switching between profiles, the customer service mailbox can be added to her profile so that she can see its contents but she must understand that replying to messages in the customer service mailbox while she is logged on to her own Outlook profile will result in those messages being retained in her own sent folder. Now there is nothing preventing her from moving the replies from her sent folder to the sent customer service sent folder but it relies on her rememering to do so which will likely favor inconsistent results.
Lastly, Outlook Web Access is installed by default, so she can check the customer service account using its credentials or hers, provided she has permission to the mailbox in AD. This will prevent her from having to switch Outlook profiles. Of course, these options are not mutually exclusive. You can implement both and this way, she has options to choose from.