SOT convergence of the operator

Let $H_n$ be a Hilbert space for all $n \in \mathbb{N}$.

Let $\alpha \in \mathbb{C}$. Consider linear operator $A_m(\alpha) \colon \bigoplus_{k=1}^m H_k\rightarrow \bigoplus_{k=1}^m H_k$ given by $A_m(\alpha) \bigoplus_{k=1}^m f_k = \bigoplus_{k=1}^{m-1} f_k \oplus |\alpha|\|f_m\| f_m $.

Can we say anything about the SOT limit of this operator i.e. that is an operator $A$ such that $\|A_m f - Af\| \to 0$ as $m\to \infty$. Thank you for any help.

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