This is most likely not a forum-type question, as there should be a definitive answer rather than just opinions. But to get a definitive answer, I think you may need to explain this part better.

I annotated a phylogenic tree in a .treefile but I can't open the exported annotated .treefile which I saved as a different file.

Based on the limited explanation you gave, I suspect that you have a Nexus file. Since all tree files are plain text, you should be able to open them in any text editor and verify. This is how Nexus files may look like:

#NEXUS
BEGIN DATA;
 DIMENSIONS NTAX=115 NCHAR=15338;
FORMAT DATATYPE=PROTEIN INTERLEAVE=yes GAP=-;

Or like this:

#NEXUS
[ID: 8939877847]
begin taxa;
        dimensions ntax=115;
        taxlabels

FigTree should be able to read Nexus files, which could mean that the one you have is somehow malformed.

Sorry about the categorisation. Yes, it is a nexus file. The phylogenetic tree was generated with iQTree and then I added annotations with Figtree.

On inspecting the file again, I added the "end" command to the tree block and now Figtree opens the file but doesn't show the annotations even though the nexus file contains a figtree block.