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We present new joint XMM-Newton and NuSTAR observations of APM 08279+5255, a gravitationally-lensed, broad-absorption line quasar ($z=3.91$). After showing a fairly stable flux ($f_{\rm2-10}\simeq4-5.5\times10^{-13}\rm~erg~s^{-1}$) from 2000 to 2008, APM 08279+5255 was found in a fainter state in the latest X-ray exposures ($f_{\rm2-10}\simeq2.7\times10^{-13}\rm~erg~s^{-1}$), which can likely be ascribed to a lower X-ray activity. Moreover, the 2019 data present a prominent Fe K$α$ emission line and do not show any significant absorption line. This fainter state, coupled to the first hard X-ray sampling of APM 08279+5255, allowed us to measure X-ray reflection and the high-energy cutoff in this source for the first time. From the analysis of previous XMM-Newton and Chandra observations, X-ray reflection is demonstrated to be a long-lasting feature of this source, but less prominent prior to 2008, possibly due to a stronger primary emission. The estimated high-energy cutoff ($E_{\rm cut}=99_{-35}^{+91}$ keV) sets a new redshift record for the farthest ever measured and places APM 08279+5255 in the allowed region of the compactness-temperature diagram of X-ray coronae, in agreement with previous results on high-$z$ quasars.