The correlative ᴹQ. sainen appeared in Demonstrative, Relative, and Correlative Stems (DRC) from 1948 (PE23/111), a combination of ᴹQ. sa “that [anaphoric]” and the instrumental suffix ᴹQ. -nen.
Neo-Quenya: For purposes of Neo-Quenya I would update this to ᴺQ. sanen “by that means (mentioned)” to be more consistent with the later use of singular instrumentals in correlatives: Q. sinen “by this means”.
In Tolkien’s later writings, the word sa is typically used as a neuter pronoun “it”, but occasionally it is used instead as a demonstrative pronoun or subordinating conjunction “that”, in phrases like ecë nin care sa “I can do that” (VT49/20) or merin sa haryalyë alassë nó vanyalyë Ambarello “I hope that you have happiness before you pass from the world” (Merin Sentence). As a subordinating conjunction, I would limit its use to clauses describing facts serving as the object of the main clause: “I know that..., I say that..., I hope that...”.
As a demonstrative pronoun I would use sa to mean “that (previously mentioned)” as opposed to ta “that (over there, not previously mentioned)”. The latter use extends to correlative combinations, such as sanomë “that place (previously mentioned)” vs. tanomë “that place (over there)”. There may be occasional confusion with sa “it”, but in most cases the meaning will be the same: cenin sa “I see it” vs. “I see that (previously mentioned)”.
See the entries on relative pronouns, demonstrative pronouns, and correlatives for further discussion.