I'm not sure where the final destination is for your graph, but here is one way to do it. First, generate your output using the ODS WORD destination. Here is an example:
ods _all_ close;
ods word file="class.docx";
ods graphics / outputfmt=svg;
proc sgplot data=sashelp.class;
scatter x=weight y=height / datalabel=name;
run;
ods _all_ close;
Next, open the file in Microsoft Word. Right-click on the graph and select, "Convert to Shape". You can then edit and move your labels. Then, deselect the graph, right-click on it, and select, "Save as Picture". This image will external save your edits as a PNG image.
Hope this helps!
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