The " OSRAM Fotodiode TO-39 1100 nm 55 ° BPX 61" for 12,60 Euros would work fine, but seems a bit expensive.
If the flash duration is 80 ms, you may be able to use the Arduino analog read function (use the internal 1.1V AREF) with the naked diode in photovoltaic mode. Note the "reversed polarity" compared to the diode symbol:
Otherwise, you may need an op amp transimpedance amplifier:
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It will be very helpful to use an IR filter or other means of excluding extraneous light.