"ti ricorderò" is correct and quite similar in meaning to "mi ricorderò di te".
- " ̶i̶o̶ ̶r̶i̶c̶o̶r̶d̶e̶r̶ò̶ ̶d̶i̶ ̶t̶e̶ ̶p̶e̶r̶ ̶s̶e̶m̶p̶r̶e" ← wrong
"io ricorderò di te" is not a wrong phrase, but rarely usable.
- io ricorderò di te i tuoi occhi azzurri e il tuo sorriso = io mi ricorderò dei tuoi occhi azzurri e del tuo sorriso (I will remember your blue eyes and your smile)
ngueza: "I will forever be in your debt" and "I will be in your debt forever" aren't saying the same thing. It's a question of where the adverb is placed. The first is saying that I will always appreciate what you did for me; you're expressing thankfulness for what the person did. The second sentence is saying that no matter how much you try to or do repay the person, the debt will never end; it'll always be there.
if there is a preposition you must always use "te"
"Ti" goes immedately before the verb
- io mi ricorderò di te = io ti ricorderò = I'll remember you
- io penso a te = io ti penso = I think of you
- io parlo con te = io ti parlo = I speak with you
- io cucino per te = io ti cucino = I cook for you
"I will forever remember you" should be an acceptable answer but according to DL it isn't. In English and Italian adverbs can be placed before, in between, or after the verb, adverbial phrases cannot. "Per sempre" is an adverbial phrase in Italian, ergo, it cannot be placed in between the auxiliary (will) and main verb (remember). However, the English translation of "per sempre" is the adverb "forever" and as such it would be proper to place it between the auxiliary and main verb. Wouldn't you agree DL and if not, why not?