HIP 65426 b is a recently discovered exoplanet imaged during the course of the SPHERE-SHINE survey. Here we present new $L$ and $M$ observations of the planet from the NACO instrument at the VLT from the NACO-ISPY survey, as well as a new $Y-H$ spectrum and $K$-band photometry from SPHERE-SHINE. Using these data, we confirm the nature of the companion as a warm, dusty planet with a mid-L spectral type. From comparison of its SED with the BT-Settl atmospheric models, we derive a best-fit effective temperature of $T_{text{eff}}=1618pm7$ K, surface gravity $log g=3.78^{+0.04}_{-0.03}$ and radius $R=1.17pm0.04$ $R_{text{J}}$ (statistical uncertainties only). Using the DUSTY and COND isochrones we estimate a mass of $8pm1$ $M_{text{J}}$. Combining the astrometric measurements from our new datasets and from the literature, we show the first indications of orbital motion of the companion (2.6$sigma$ significance) and derive preliminary orbital constraints. We find a highly inclined orbit ($i=107^{+13}_{-10}$ deg) with an orbital period of $800^{+1200}_{-400}$ yr. We also report SPHERE sparse aperture masking observations that investigate the possibility that HIP 65426 b was scattered onto its current orbit by an additional companion at a smaller orbital separation. From this data we rule out the presence of brown dwarf companions with masses greater than 16 $M_{text{J}}$ at separations larger than 3 AU, significantly narrowing the parameter space for such a companion.
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