  HR2562 is an F5V star located at ~33 pc from the Sun hosting a substellar
companion that was discovered using the GPI instrument. The main objective of
the present paper is to provide an extensive characterisation of the substellar
companion, by deriving its fundamental properties. We observed HR 2562 with the
near-infrared branch (IFS and IRDIS) of SPHERE at the VLT. During our
observations IFS was operating in the YJ band, while IRDIS was observing with
the $H$ broad-band filter. The data were reduced with the dedicated SPHERE GTO
pipeline, which is custom-designed for this instrument. On the reduced images,
we then applied the post-processing procedures that are specifically prepared
to subtract the speckle noise. The companion is clearly detected in both IRDIS
and IFS datasets. We obtained photometry in three different spectral bands. The
comparison with template spectra allowed us to derive a spectral type of T2-T3
for the companion. Using both evolutionary and atmospheric models we inferred
the main physical parameters of the companion obtaining a mass of
32+/-14$~MJup, T_{eff}=1100+/-200 K and log(g)=4.75+/-0.41.
