The consonantal shifts which Sivan finds in
Northwest Semitic Vocabules and which apply to shemesh (shamash) are

P > M and  S > SH

Hebrew SHAMESH = South Arabic SHFSH = Ugaritic SHPSH

The latter is attested as SHAPSHU
in the Northwest Semitic evidence (SH-AP-SHU).

SHAPSHU (based on consonantal shifts identified by Sivan, i.e. p>m)
would have become SHAMASH

Sivan also found SAPSU corresponding to the attested personal name SHAW-SHA i.e. Latvian SAU.SA "heat, dry"
and hence with a different ending Latvian SAU.LE,
i.e. proto-Indo-Euroepan *SAW.LE or *SUE.EN "sun".

Since S went to SH in Northwest Semitic and the dipthong AW- was
contracted in this period acording to Sivan, we also can see that the
Indo-European reconstructed form *SAW- for the sun
is older than SHAMAS.
Hence the root for "sun" was originally a single syllable.

This analysis is supported by Hebrew SHA.CHAR (SSHR) "dawn, sun.rise" where CHAR is Latvian CEL "rise" so that when we examine SHA.MASH "sun" this must mean "midday" or "heaven" or "mid-heaven" (i.e. also SUM.MER - i.e. the sun at seasonal mid-heaven, which the linguists have reconstructed as Germanic *SUMMARAZ).

In Pharaonic Egyptian, the initial sibilant went from SS to R (much as Latvian AUSS went to English EAR) and this is then SHMSH > RMSH or RA.MESH, i.e, RA.MESIS "the sun in culmination, meridian, of the sun".