wholegrainBut can you say: He is very rich, having many investments abroad, having many contacts abroad.
You can say it, but normally you wouldn't. You would only say this if you were deliberately seeking a distinctive stylistic effect. The sense of linked cause-and-effect does not successfully carry through the sentence in the way that I think you are imagining.
wholegrainunlike what you can do with (because/since he has)?
"He is very rich since/because he has many investments abroad since/because he has many contacts abroad."
This is the same deal: normally you wouldn't say it, but you might, rarely, for special effect.