To simplify the given expression, let's denote it in a more manageable way.

We have:

\[
\frac{[a^2 - (b+c)^2](a + b - c)}{(a + b - c) [a^2 - (b+c)^2] (a+b-c)} \cdot \frac{1}{(a^2 + c^2 - 2ac - b^2)}
\]

We can simplify the expression step by step.

1. **Cancelling Identical Terms**: The term \((a + b - c)\) appears in both the numerator and the denominator. Assuming \(a+b-c \neq 0\), we can cancel it out.

The expression simplifies to:

\[
\frac{a^2 - (b+c)^2}{(a^2 - (b+c)^2)(a + b - c)(a^2 + c^2 - 2ac - b^2)}
\]

2. **Cancelling Again**: We notice that \(a^2 - (b+c)^2\) can also be cancelled out, given \(a^2 - (b+c)^2 \neq 0\).

Now, we obtain:

\[
\frac{1}{(a + b - c)(a^2 + c^2 - 2ac - b^2)}
\]

3. **Simplifying the Remaining Component**: The second term in the denominator can further be simplified. Notice that:

\[
a^2 + c^2 - 2ac - b^2 = (a - c)^2 - b^2
\]

Therefore, we can rewrite the expression as:

\[
\frac{1}{(a + b - c) \left((a - c)^2 - b^2\right)}
\]

Putting it all together, the fully simplified expression is:

\[
\frac{1}{(a + b - c) \left((a - c)^2 - b^2\right)}
\]

Thus, this is the simplified form of the original expression, assuming all variables and terms are appropriately defined and non-zero where necessary.