After a long time of having this option disabled (or simply not available) we can now send our Tumblr posts to a Facebook Page once again (We talk about Pages here, Not Profiles).
- Go To Blog Settings » Check Share posts on your Timeline
- After you log in to Facebook you will see a message that says: Tumblr would also like permission to: Manage your pages Tumblr may login as any of your X Pages, including: (A list with your Pages). Click on Allow.
- Now, Go Back to your TUMBLR and go to Blog Settings » Scroll Down and, from the dropdown menu (that was not there before) choose which page (or profile) you will send your posts to.
Source: Send Tumblr Posts to Facebook Pages.