Coordinated observations obtained during the JOP12 (Joint Observing Programme between SOHO and ground-based instruments) allow us to analyse the physical conditions in a prominence of 5 June 1997 and its environment in the solar corona. The arch-shaped prominence shows either vertical or horizontal structures according to the observed lines (H alpha with the coronagraph of the Wroclaw University Observatory at Bialkow and lines in a broad temperature range by the Coronal Diagnostic Spectrometer CDS). The less dynamic behaviour of this prominence was shown by the persistence of bubbles in the prominence and confirmed by the Dopplershifts measured in CDS lines and in Ha! by the Italian Panoramic Monochromator (IPM) filter on the THEMIS telescope in Tenerife. We explain the complex morphobgy of this prominence by recent 3D MHD models. Finally, we present prominence spectra in higher lines of the hydrogen Lyman series (from L delta to L-9), together with some other UV lines. These data have been obtained by the Solar Ultraviolet Measurements of Emitted Radiation (SUMER). We demonstrate the basic characteristics of the calibrated line profiles of Lyman lines and compare them with the theoretical profiles computed from isothermal-isobaric models. This leads to some constraints on the environment of the prominence.