It may depend on which version of the RFE data you download. If you search "coordinate system" on the website, you get this page which states that the Daily datasets are in a geographic coordinate system. The Dekadal data is projected into an Albers coordinate system:
Origin of latitudes : 1.000000 deg
Central meridian : 20.000000 deg
First std parallel : -19.000000 deg
Second std parallel : 21.000000 deg
Projection = ALBERS Conical Equal-area projection uses the clarke 1866 spheroid
This is not great as "Clarke 1866 spheroid" means that they just munged the data together and lost any original GCS/datum information. Perhaps the data accuracy isn't good enough that the GCS/datum info doesn't matter. The effect of ignoring the datum information is, at most, a few hundred meters. With this data, there's not an easy way to identify how far off it is anyway versus another dataset.
First, I would define the data using the above definition. To get the GCS, look in the geographic coordinate systems\spheroid-based folder. Add the raster to a data frame, and set the data frame's coordinate system to match the Mozambique data. Ignore any datum warning messages. Do the clip now, or export the raster into the Mozambique coordinate system by right-clicking the layer in the table of contents and selecting data, export data. In that dialog, choose the data frame's coordinate system.
Another workflow is use WGS84 (or whatever GCS the Mozambique is using) when you define the Albers-based coordinate system.