There are only 2 ways, both of which require an access to  Encore :

• Exporting a midi file (but many things will be lost)

• Exporting as a MusicXML file (possible in recent version of Encore). That would be ideal.

Unfortunately, the free demo of Encore can't save, so it probably won't allow such exports : http://www.passportmusic.com/downloads/ 

If you don't have access to Encore, find someone who has it...

Or if you have too many files, reinstall Encore (if necessary, buy a recent version), and make sure that it is version 5, which can export MusicXML files.

Encore 5 for Windows exports MusicXML 1.1. Notes and some text but no expressions or lyrics. MIDI export doesn’t do text.

If you have printed copies, scanning in with SmartScore X2 Pro may be the better choice. It’s still 32 bit Only but you can run that over Win10. There’s a fully functional demo for 30 days 

https://www.musitek.com/demos.html

Finale owners get the Pro version for half off.

I have Finale 2008 which has the option to import Encore files. I've never tried it, but it should work.

>I have Finale 2008 which has the option to import Encore files. I've never tried it, but it should work.<

If I recall correctly, Encore 3.something was the last version where that worked. I don’t remember the last version of Finale that supported this. If the files are old enough and you have an old enough version of Finale, give it a try.

I think that Finale 2009 was the last version that could import Encore files. The reliability was sometimes questioned by some users.

Another idea : try Harmony Assistant (by Myriad Software, not free : 85$, 70€).

According to their website http://myriad-online.com/en/docs/diff.htm , it imports Encore files and can export in the MusicXML format.

Finale 2009 — sounds right. It wasn’t very good at it, either. For years, I did my church work in Encore because it was so fast and used Finale for anything else.

Harmony Assistant is terrible at converting Encore. Fortunately, there’s a trial period so that one can find out how truly bad it is.

One of the problems is that the current version of Encore cannot open the oldest files. One of the reasons I keep an old G4 going With OS 9/10.4 is to access my early files—it’s a 3 step conversion involving two old computers before I can open them on my working iMac Pro. I hadn’t had a church job since 2007 and recently, I acquired two. It’s handy to have my old work again. I can export the notes via MusicXML but not the lyrics.

SmartScore X2 Pro is pretty good at reading Encore printouts but the current Mac version is terrible in Mojave and doesn’t work at all in Catalina. 64 bit versions of SSX2P and Encore have been promised for a long time — we’re still waiting.

Another here has offered to scan a couple of my Encore charts but I do have an old Windows laptop and can install SmartScore onto it if I’m desperate to scan in all my old work. I’m way, way too busy for that. Again, that’s the best way to get them into Finale if you have printouts and lots of lyrics are involved.

Encore is still around as you know. I show up now and then in the users’ forum to help now and then but it’s a ghost town. You can contact them and see if they have a download available for your old version and upgrade an old license and export the XML. Be prepared to re-enter lyrics and expressions.

Update:

I just got off the phone with Don Williams, Encore's original developer and owner/developer of SonicScores/Overture—he and I have been in touch for awhile. He has completed the purchase of all code and IP of PassportDesigns and will soon re-launch the passportdesigns.com web site.

It appears that Encore is going to be raised from the dead. Plans include 64 bit for Mac/Win, MusicXML 3.0 import/export, multiple undo and possibly a few other features. The immediate goal is to get it working and reading older files so that longtime users can access them and export if desired. 

At the moment, I have no other details nor do I have a timeline.