Learn Farsi: اگر فرستنده کارتن را بیاورد، فردا به مقصد می‌فرستمش. - If the sender brings the carton, I will send it to the destination tomorrow.

Because it follows اگر (if). In Farsi first conditionals (situations that are likely or possible in the future), the 'if' part of the sentence must use the Present Subjunctive. Here, بیـ + آور (present root of 'to bring') + ـَد (he/she/it ending) makes the subjunctive form بیاورد.

The translation says 'I will send it,' but isn't می‌فرستم in the present tense?

Yes, می‌فرستم is the Present Indicative. In Farsi, the simple present tense is very commonly used to talk about the future, especially in the result half of an 'if' sentence, or when you already have a future time word like فردا (tomorrow) in the sentence.

What is the ـش at the very end of می‌فرستمش?

That is the attached pronoun meaning 'him,' 'her,' or 'it.' Here it means 'it' and refers back to the carton (کارتن). Instead of using a separate word for 'it' as the object, Farsi often just attaches ـش to the end of the verb.

The words for 'sender' (فرستنده) and 'I send' (می‌فرستم) look similar. Are they connected?

Yes! They share the same present stem: فرست (ferest). If you add the suffix ـنده (-ande) to a present stem, it creates a noun for the person who does that action. So فرست (send) + ـنده = (sender).