Internal motions in femtosecond soliton molecules provide insight into universal collective dynamics in various nonlinear systems. Here we introduce an orbital-angular-momentum (OAM)-resolved method that maps the relative phase motion within a femtosecond soliton molecule into the rotational movement of the interferometric beam profile of two optical vortices. By this means, long-term relative phase evolutions of doublet and triplet soliton molecules generated in an all-polarization-maintaining mode-locked Er-fiber laser are revealed. This simple and practical OAM-resolved method represents a promising way to directly visualize the complex phase dynamics in a diversity of multisoliton structures.