The progenitor systems of type Ia supernovae and gravitational wave sources are believed to arise from a mass transfer process known as common envelope (CE) evolution. Although a large fraction of binary systems will undergo CE evolution, the detailed physics remains poorly understood, largely due to the lack of observed benchmark systems where both the pre-CE and post-CE conditions are known. While post-CE systems containing a white dwarf (WD) and main-sequence (MS) star have been observed, they are located in the field, making it difficult to gain insights into their pre-CE parameters. Finding post-CE systems in star clusters can provide an independent constraint on the binary's age, but only two WD+MS post-CE systems in a star cluster have ever been found. Recently, a new WD+MS post-CE system was discovered in the Alessi 12 cluster. Alessi12-PCE is an ideal candidate to study CE evolution as it (i) is a cluster member, (ii) is a confirmed short-period binary and (iii) has clear spectral features of both a WD and a MS star in an optical spectrum. However, while spectral features at optical wavelengths can measure a WD's temperature and surface gravity (and thus its mass), there are systematic uncertainties that can have a significant impact on the inferred pre-CE conditions. Thus, we request 4 orbits with HST COS to obtain an ultraviolet spectrum to measure the effective temperature and surface gravity of Alessi12-PCE from its Lyman-alpha feature and use this measurement to refine the precision on the WD's mass. Alessi12-PCE will be just the third WD+MS post-CE binary ever identified in a star cluster, highlighting the necessity of this data.