See How you can Change Email on Facebook

Facebook permits you to make changes to your primary email address, or the one you used to log in and also receive Facebook notifications. Changing your primary email address is as simple as making a few edits to your settings from either your computer or mobile device.You can change the email address linked to your Facebook account from any device connected to the internet.

It is advisable to do this if your Facebook account has been breached or hijacked. You can also decide to do it if you change email providers, and for many other reasons. Whatever the case may be, there are two steps to complete; you need to add the new email address you would like to use, and then configure it so it becomes the primary address.

How to Change Email on Facebook 

With a Computer

You can change your email address from any computer, be it Mac-based or Windows-based, using any Web browser. That could be Internet Explorer or Edge on a PC, Safari on a Mac, or any compatible third-party browser you've installed like Firefox or Chrome.

To change the email address you use with Facebook and to set it as the primary address from a computer:

• Go to www.facebook.com and log in.
• Tap on the drop down arrow. The button is located at the top-right hand corner of your screen. It will open a new menu, select 'Settings'. 
• From the General tab, select 'Contact'.
• Select 'Add Another Email Or Mobile Number To Your Email Account'.
• Type the new address you want to add and click 'Add'.
• Enter your Facebook password and click Submit.
• Click Close.
• Check your email and click on 'Confirm' to verify that you made this change.
• Login to Facebook when prompted.
• Select 'Contact' again (as noted in Step 3).
• Select the new address and click 'Save Changes' to make it your primary email.

N/B: If you want to, You can remove the old email address by following steps 1-3 above and choosing the email to remove.

iOS

• Click on the Facebook app.
• Click on the menu button. This is the three horizontal lines in the lower right corner of your screen.
• Click on 'Settings'. It's at the very bottom of the page
• Click on 'Account Settings'.
• Click on 'General'.
• Click on 'Email'.
• Click on 'Add Email Address' to add an email.
• Put in your email and password into the boxes provided.
• Click on 'Add Email'. This email will be added to the list of emails that are linked to your Facebook.
• Click on Primary Email to change your primary email. You will be brought to a page where you can tap on any of the emails you have on record to make that email as your primary. This is the email that Facebook uses to contact you if you have email notifications, as well as the email you will use to login to Facebook.
• After Clicking on on your preferred primary email, type your Facebook password into the box below and click on 'Save'.

Android 

If you use Facebook on your Android device and have the Facebook app you can make an email address change there. This is how to add a new email address and also set it as your primary address using the Facebook app:

• Select the Facebook app icon to open the app.
• Tap on the three horizontal lines at the far right side of the top navigation bar.
• Scroll to click 'Account Settings'.
• Tap on 'General', and then 'Email'.
• Click 'Add Email Address'.
• Type the address you want to add and click on 'Add Email'. If you're prompted to put in your Facebook password, do so.
• Click on 'Add Email Address'.
• Check for an email from Facebook on your phone’s Mail app and click Confirm to verify you made this change.
• Log back in to Facebook.
• Go to' Account Settings', then' General', then 'Email'.
• Click on 'Primary Email'.
• Select the new email address, type in your Facebook password, and then click on 'Save' to make it your primary email.