The metal abundances in the atmospheres of hot white dwarfs (WDs) entering the cooling sequence are determined by the preceding Asymptotic Giant Branch (AGB) evolutionary phase and, subsequently, by the onset of gravitational settling and radiative levitation. In this paper, we investigate three hot He-rich WDs, which are believed to result from a late He-shell flash. During such a flash, the He-rich intershell matter is dredged up and dominates the surface chemistry. Hence, in contrast to the usual H-rich WDs, their spectra allow direct access to s-process element abundances in the intershell that were synthesized during the AGB stage. In order to look for trans-iron group elements (atomic number Z>29), we performed a non-local thermodynamic equilibrium model atmosphere analysis of new ultraviolet spectra taken with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope. One of our program stars is of PG1159 spectral type; this star, PG1707+427, has effective temperature Teff=85,000 K, and surface gravity logg=7.5. The two other stars are DO white dwarfs: WD0111+002 has Teff=58,000 K and logg=7.7, and PG0109+111 has Teff=70,000 K and logg=8.0. These stars trace the onset of element diffusion during early WD evolution. While zinc is the only trans-iron element we could detect in the PG1159 star, both DOs exhibit lines from Zn, Ga, Ge, Se; one additionally exhibits lines from Sr, Sn, Te, and I and the other from As. Generally, the trans-iron elements are very abundant in the DOs, meaning that radiative levitation must be acting. Most extreme is the almost six orders of magnitude oversolar abundance of tellurium in PG0109+111. In terms of mass fraction, it is the most abundant metal in the atmosphere. The two DOs join the hitherto unique hot DO RE0503-289, in which 14 trans-iron elements had even been identified.