Neologism! This text is a neologism, which means that it was not composed by Tolkien himself. The content presented herein should therefore always be considered as experimental and subject of debate.
Consider Elaran the author of this work.
A more plausible alternative to a problematic yet often used Neo-Sindarin phrase.
The phrase **hannon le comes from the Lord of the Rings film trilogy. David Salo, the linguist who prepared the Quenya and Sindarin material for these films, reconstructed the verb **hanna- "to thank" likely around the year 2000. But the story of this reconstruction goes back to 1980, to the publication of the Unfinished Tales. In this book, we see the word Eruhantalë with its meaning "Thanksgiving to Eru", and it would be safe to assume that hantalë means "thanksgiving" by itself. It is also rather clear that the final element of this word is the abstract noun suffix, -lë, which Quenya is known to employ and form nouns from verbs. Thus, we reach the Quenya verb *hanta-, meaning "to give thanks".
Since we have the Quenya verb, we can now try and reconstruct it for Sindarin. This means that we will use the phonetic development rules that concern Sindarin (rather than Quenya) as we derive it from Primitive Quenderin. But in the early 2000s, we had no documents in which a PQ root for this verb was shared. Then we need to guess what its root may be, and back then the only attested root which supports it phonetically was √KᴴAN, despite its unfitting meaning "to understand". Having almost no other option at the time, Salo might have used this root and assumed that it might have had a semantic shift during its journey to Sindarin (and also to Quenya *hanta- "to give thanks"). Now, without going into great detail on the development stages: Ancient kʰ- is found as h- in both Quenya and Sindarin: √KᴴER > Q. heru ⪤ S. hîr. Meanwhile -nt- in Quenya words is often found as -nn- in Sindarin: Q. panta- ⪤ S. panna-. In conclusion, given the lack of attested material at the time, reconstructing Quenya *hanta- as Neo-Sindarin **hanna- was an arguably safe approach. However, in 2002, the 43rd issue of Vinyar Tengwar shared the root √HAN "add to, increase, enhance, honour (espec. by gift)" which fits much better with Q. *hanta- in terms of its meaning. And this is where the problems arise, because in 1994 we were told:
PQ h- only survived in the dialects of Aman. It disappeared without trace in Sindarin. [HoME-XI/365]
If the root for this verb is √HAN, and if ancient h- disappeared in Sindarin, then our verb must be *anna- instead. This is a problem, because we already have anna- attested as "to give, add to". But then comes the 22nd issue of Parma Eldalamberon to share some of the latest linguistic writings by Tolkien, offering the Telerin verb han- "to give" as a derivation from √HAN (which likely means that han- and hanta- share the same root, as even S. anna- shows the "to add to" sense of this root). More importantly, the gerund form of the "to give" verb of Sindarin was shared as aned (which would have been *annad in earlier works), and this seems to suggest that Tolkien changed anna- to be an- in his later works, derived from the same root as its Telerin cognate. And so we can argue that *anna- is free to use as "to give thanks", especially since we see both han- and *hanta- in the languages of the Blessed Realm (thus supporting that Sindarin could also use "an- & anna-" as separate verbs from the same root).
Now, we may attempt to use *anna- "to give thanks" in a phrase to say "thank you". For this, we would need "you" in dative form, as analogues like ón annin show us. And while Tolkien did use le (which is the formal/polite second person pronoun) as dative, its form actually appears to be nominative, arguably used as an "absolute form" (which could function as both accusative and dative) as his gloss "[to] you" may suggest with the brackets. On the other hand, the actual dative form of le is somewhat unclear, but the current approach in Tolkienian Linguistics communities is to use *allen "to you", based on attested examples like annin "to me" and ammen "to us". Thus, we get:
I give thanks to you!
Please keep in mind that this is not meant to be an "absolutely correct" form of giving thanks in Sindarin, although it is an arguably better alternative to **hannon le. Even its creator Salo would not disagree with the issues of the old phrase, due to more recent evidence to the contrary. And the same could happen with this new alternative, along with all other works which concern Neo-Quenya and Neo-Sindarin. Everything is and will remain subject to change until their direct attestation in the posthumously published works of Tolkien, which are currently being edited by the Elvish Linguistic Fellowship for publication in linguistic journals like Vinyar Tengwar and Parma Eldalamberon.