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We proved that every ICE-closed subcategory (resp. epibrick, monobrick) in $\\mathcal{A^{'}}$ or $\\mathcal{A^{''}}$ can be extended to an ICE-closed subcategories (resp. epibrick, monobrick) in $\\mathcal{A}$, and the assignment $\\mathcal{C}\\mapsto j^*(\\mathcal{C})$ defines a bijection between certain ICE-closed subcategories in $\\mathcal{A}$ and those in $\\mathcal{A}''$. 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We proved that every ICE-closed subcategory (resp. epibrick, monobrick) in $\\mathcal{A^{'}}$ or $\\mathcal{A^{''}}$ can be extended to an ICE-closed subcategories (resp. epibrick, monobrick) in $\\mathcal{A}$, and the assignment $\\mathcal{C}\\mapsto j^*(\\mathcal{C})$ defines a bijection between certain ICE-closed subcategories in $\\mathcal{A}$ and those in $\\mathcal{A}''$. 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