The statement $$B \Rightarrow ((\neg A) \vee B)$$ is not equivalent to:

The statement $$B \Rightarrow ((\neg A) \vee B)$$ simplifies as follows: $$B \Rightarrow (\neg A \vee B) \equiv \neg B \vee (\neg A \vee B) \equiv \neg A \vee (\neg B \vee B) \equiv \neg A \vee T \equiv T.$$ Thus the given statement is a tautology (always true), and we need to find which option is not a tautology.

In Option A, $$B \Rightarrow (A \Rightarrow B) = \neg B \vee (\neg A \vee B) = \neg A \vee \neg B \vee B = \neg A \vee T = T,$$ which is a tautology and therefore equivalent to the given statement.

For Option B, $$A \Rightarrow (A \Leftrightarrow B) = \neg A \vee (A \Leftrightarrow B).$$ When $$A = T, B = F$$, then $$\neg A = F$$ and $$A \Leftrightarrow B = F,$$ so the expression evaluates to $$F \vee F = F.$$ Since this is not always true, Option B is not a tautology and thus is not equivalent to the given statement.

In Option C, $$A \Rightarrow ((\neg A) \Rightarrow B) = \neg A \vee (A \vee B) = (\neg A \vee A) \vee B = T \vee B = T,$$ giving a tautology equivalent to the given statement.

Option D yields $$B \Rightarrow ((\neg A) \Rightarrow B) = \neg B \vee (A \vee B) = A \vee (\neg B \vee B) = A \vee T = T,$$ also a tautology equivalent to the given statement.

Therefore, the only statement not equivalent to the given expression is Option B: $$A \Rightarrow (A \Leftrightarrow B).$$