In Quenya when the voiced stop g became spirantal ʒ [ɣ], the resulting spirant generally vanished. This sound change is distinct from the much more ancient vanishing or ʒ (or h) in Primitive Elvish. Tolkien gave essentially the same description of this sound change in both the Outline of Phonetic Development (OP1) from the 1930s and the Outline of Phonology (OP2) from the 1950s, but with more details in OP2:

g probably became [ʒ] but this stage was already past in early classical PQ. Initially in AQ and early PQ the sign h was used. It appears to have represented the “clear beginning” (or smooth breathing). But it soon disappeared (OP1: PE19/32).

g became at first the open spirant ʒ, with weak friction. But except initially this sound had already disappeared in Parmaquesta. Initially in early Parmaquesta g > ʒ was still represented by the sign [h]. This may be transcribed with [’], as ’ondo “stone”, since it denoted the “clear beginning” or sharp glottal opening, not shown by original initial vowels. But this sound was lost and its representation given up in normal or classical PQ. The same situation obtained in AQ. But the Rumilian alphabet contained a sign for [ʒ], and it appears that in archaic Quenya this sound, as product of g, still persisted (OP2: PE19/70).

As these notes indicate, it seems that ʒ still existed in Ancient Quenya [AQ] at the time the Sarati alphabet was used, but only barely existed by early Parmaquesta [PQ], lingering only as something like a glottal stop [ʔ] at the beginning of words, but this “clear beginning” sound was soon lost. The tengwa h lost its original function, and its name anna seems to have nothing to do with its original sound. In alternate tengwar modes, h was repurposed to represent vowels, and in Quenya its only remaining function seems to be as a carrier for the underdots used to represent an independent y sound: hÍ.

Note that where ʒ disappeared between vowels, the two vowels only combined when identical (aʒa > ā) or produced a normal diphthong (aʒi > ai); other combinations produced disyllabic vowels in hiatus (OP1: PE19/63; OP2: PE19/70-71). Examples include ✶wegō(n) > Q. vëo “living creature” (PE17/189) or ✶rīgā > Q. ría “garland” (PM/347). As shown by the second example, this could even leave a long vowel in hiatus with a short one. Where two short vowels were left in hiatus, Tolkien often indicated this by placing a dieresis (¨) on the first of the pair.

As suggested in the entry on how [lɣ], [rɣ] became [ll], [rr], it is possible ʒ lingered longer in the combinations lʒ, rʒ, since these had divergent developments in the Ñoldorin and Vanyarin dialects of Quenya (to ll, rr and lg, rg, respectively). Assuming this is true, how these might have been represented in Tengwar isn’t clear.

Conceptual Development: The Early Qenya phonetic developments are complicated by the existence of an entire series of voiced spirants in Primitive Elvish in the 1910s and 1920s (rather than just isolated primitive ʒ as in the mid-1930s forward). The medial voiced stops merged with this voiced spirant series in the Kor-Eldarin period in Early Qenya (PE12/15-16). Thus medial g > ʒ > (nil), for example: ᴱ✶nēgittĕ > ᴱQ. neite “wax” (GL/60). However, initial voiced stops were unvoiced, so that g- > k-, such as: ᴱ✶gṛþ- > ᴱQ. karda- “to admire” (GL/42) and ᴱ✶grgu- > ᴱQ. karko “alimentary canel” (PE13/144). Original primitive initial ʒ- did generally vanish in Early Qenya, however, as in: ᴱ✶ʒolwḗ > ᴱQ. olwe “a stink” (PE13/145).