Step 1: Understanding the Concept:
This question focuses on the heritability of morphological fruit traits in mango (*Mangifera indica*) breeding.
Certain cultivars possess highly heritable, dominant physical traits that are consistently passed down to their hybrid offspring.
Step 2: Detailed Explanation:
Let us analyze the distinct physical traits of the listed mango cultivars:
1. Totapuri:
Also known as 'Bangalora' or 'Collector,' Totapuri is a commercial mango cultivar widely grown in Southern India.
It is easily recognized by its distinct oblong shape with a prominent, beak-like hook at the tip of the fruit.
Genetic studies in mango breeding show that this "beak" character is a highly dominant morphological trait.
When Totapuri is used as a parent in crosses (such as in the parentage of the hybrid variety 'Manjeera,' which is Rumani $\times$ Neelum, or other targeted crosses), it consistently imparts this beak-like tip to its hybrid progenies.
2. Manjeera, Banganpalli, Amrapali:
While these are important commercial cultivars or hybrids, none of them serve as the primary source or donor for the beak-like fruit shape.
Instead, they have different fruit shapes (e.g., Banganpalli is obliquely oval, and Amrapali is oblong-sigmoid).
Step 3: Final Answer:
The mango cultivar that imparts a prominent beak character to its progenies is Totapuri.
This matches Option (B).