Spiral arms, rings and large scale asymmetries are structures observed in high resolution observations of protoplanetary disks, and it appears that some of the disks showing spiral arms in scattered light also show asymmetries in millimeter-sized dust. HD~135344B is one of these disks. Planets are invoked as the origin of these structures, but no planet has been observed so far. We investigate the nature of the asymmetric structure in the HD~135344B disk in order to understand the origin of the spirals and of the asymmetry seen in this disk. Ultimately, we aim at understanding whether or not one or more planets are needed to explain such structures. We present new ALMA sub-0.1" resolution observations in Band 3 and 4. The high spatial resolution allows us to characterize the mm-dust morphology of the disk. The low optical depth of continuum emission probes the bulk of the dust in vortex. Moreover, we combine the new observations with archival data to perform a multi-wavelength analysis and to obtain information about the dust distribution and properties inside the asymmetry. We resolve the asymmetric disk into a symmetric ring + asymmetric crescent, and observe that: (1) the spectral index strongly decreases at the center of the vortex, consistent with the presence of large grains; (2) for the first time, an azimuthal shift of the peak of the vortex with wavelength is observed; (3) the azimuthal width of the vortex decreases at longer wavelengths, as expected for dust traps. These features allow to confirm the nature of the asymmetry as a vortex. Finally a lower limit to the total mass of the vortex is $0.3MJupiter$. Considering the uncertainties involved in this estimate, it is possible that the actual mass of the vortex is higher and possibly within the required values ($\sim 4MJupiter$) to launch spiral arms similar to those observed in scattered light.