We plan to upgrade from Tridion 2013 SP1 to WEB 8.5. Could you please let us know if DD4T 1.3 JAVA is still supported if upgrade to WEB 8.5. I know you would suggest to upgrade to version 2 but the CD part is not managed by our team. Please let us know and thank you in advance.
SDL Web 8.5 is fully backwards compatible with SDL Tridion 2013 SP1, so along that line, DD4T 1.3 should also still work with it. DD4T is using a provider model to connect to Tridion/SDL Web. I don't think anybody actually created a provider for Web 8.5 for DD4T 1.3, but that is something you can do yourself (in .NET I know you don't even have to but can use assembly binding redirects to the correct version, not sure how that is handled in Java).
However please note that DD4T 1.3 might be using unsupported features which worked in 2013 SP1, which aren't there in SDL Web 8.5 anymore (like direct database queries). I unfortunately don't know enough detail if that is the case or not, that is something you will have to investigate yourself.