The level structure of the neutron-rich 69Cu,71Cu, and Cu73 isotopes has been investigated by means of multinucleon transfer reactions. The experiment was performed at Laboratori Nazionali di Legnaro using the AGATA Demonstrator array coupled to the PRISMA magnetic spectrometer. Lifetimes of excited states in Cu nuclei were measured with the recoil-distance Doppler-shift method. The resulting electromagnetic matrix elements for transitions from excited states in Cu69,71,73 nuclei are used to assess the collective or single-particle character of these states. The results are compared with predictions of large-scale shell-model calculations, giving further insight into the evolution of the proton pf shell as neutrons fill the 1g9/2 orbital.