Integrated photonic devices have become pivotal elements across most research fields that involve light-based applications. A particularly versatile category of this technology are programmable photonic integrated processors, which are being employed in an increasing variety of applications, like communication or photonic computing. Such processors accurately control on-chip light within meshes of programmable optical gates. Free-space optics applications can utilize this technology by using appropriate on-chip interfaces to couple distributions of light to the photonic chip. This enables, for example, access to the spatial properties of free-space light, particularly to phase distributions, which is usually challenging and requires either specialized devices or additional components. Here we discuss and show the detection of amplitude and phase of structured higher-order light beams using a multipurpose photonic processor. Our device provides measurements of amplitude and phase distributions which can be used to, e.g., directly distinguish light's orbital angular momentum without the need for further elements interacting with the free-space light. Paving a way towards more convenient and intuitive phase measurements of structured light, we envision applications in a wide range of fields, specifically in microscopy or communications where the spatial distributions of lights properties are important.