So I am wondering is there any references for this theorem?
The three articles referenced presented in logical order of exposition are respectively
Faltings, Gerd Hodge-Tate structures and modular forms Math. Ann. 278 (1987)
Tsuji, Takeshi $p$-adic étale cohomology and crystalline cohomology in the semi-stable reduction case. Invent. Math. 137 (1999)
Saito, Takeshi Modular forms and $p$-adic Hodge theory. Invent. Math. 129 (1997)