Use SHAddToRecentDocs function with full path to the file as second parameter. Don't forget to add SHlObj in uses chapter.
uses
Shlobj;
...
procedure TForm1.Button1Click(Sender: TObject);
begin
if OpenDialog1.Execute then
Edit1.Text:=OpenDialog1.FileName;
end;
procedure TForm1.Button2Click(Sender: TObject);
begin
SHAddToRecentDocs(SHARD_PATH, PChar(Edit1.Text));
end;