Kepler wrote the two-convex recipe in Dioptrice and did not build one. Scheiner and others did, a few years on. A real image sits between the lenses, so you can put a reticle there; the view is upside down; the field is wider than Galileo’s.
Almost every astronomical refractor after that is this tube with extras. On the board: two convex glasses, focus in the gap, parallel in and out, inverted.