、。
Please remember to mail this letter tomorrow morning.
Literal
Tomorrow [possessive-の] morning, this letter [object-を] mail [nominalizer-の] [object-を] remember-in-advance please.
覚えておく combines 覚える ('to remember/memorize') with the auxiliary ~ておく ('do in advance/for future use') — 'keep something in memory for later.' Then 覚えておいてください = 'please keep it in mind.' The outer object を attaches to the nominalized clause (この手紙を投函するの), wrapping 'mailing this letter' into a noun so it can be the object of 覚える. 投函 is a more formal word for 'mailing/posting' than 出す.