"The boy is improving his letter."
Translation:Le garçon améliore sa lettre.
Wouldn't the French be more likely to say "Le garçon corrige (or fait des corrections à) sa lettre to express the idea of improving it? "améliorer une lettre" strikes me as unnatural in French.
Improving a letter can indeed include correcting spelling, but also changing the typeface and layout (or improving his hand writing), rewriting a bit for a better style, changing some words to avoid repetitions... we have no context here, but I thing that "corriger" would be a bit limited in meaning.
s'améliorer is used if the subject is improving him/herself.
As long as the subject improves something else than him/herself, you don't need the reflexive pronoun "se".
In French, the spelling is "lettre" (not letter)
And the gender is feminine: "la lettre" => "sa lettre"
I thought a letter of the alphabet is 'un lettre' but a letter is actually 'un note'.
"une lettre" is both an alphabet sign and a message written on paper you send someone.
"une note" can be a short message on paper or a simple comment or reminder you may also type in your phone or computer.
"Le" and "la" are elided (drop the vowel and replace it with an apostrophe) in front of words starting with a vowel or a mute H, in order to avoid a vowel sound conflict.
Since "garçon" starts with a consonant, please keep "le".