I don't know a possibility to share it like in linux. But I would recommend you, to install the Firefox addon Sync. It's from Mozilla itself and you can share easily your bookmarks with this addon. But you also can share many other informations, like passwords etc.(You can disable password-sharing etc. and only activate bookmarks of course)
You will have to create an account and add all accounts of your computer to sync, than you have your bookmarks available on all accounts.
Yes, it isn't really comfortable at first, but after this one-time-work you have good sync tool for firefox.
Also you can invite other devices and share your bookmarks with them.
Install Sync
- Download
Setup Sync on the first account
- In the Firefox click the Firefox-button -> Set Up Sync.
- Click Create a New Account.
Fill in your account-information
IMPORTANT STEP You have to change the option, that only your bookmarks will get synced by clicking on the Sync options-button.
- After you've edited your options, click Next.
Add second Account
Do these steps on the second account that you are trying to add to Firefox Sync.
- In the Firefox click the Firefox-button -> Set Up Sync.
- In the next window choose "I Have an Account".
- Because you want to add a second user account and not a pc choose "I don't have the device with me".
- Sign in to your Sync account.
- Click Next
- Click Finish.
Now your bookmarks will be synced between these two accounts. You also can add more accounts of course by repeating the "Add second account"-steps.