Is there a Philippine bank in China?

Yes, it's Metrobank. It has a subsidiary in China called Metropolitan Bank (China) Ltd. and is headquartered in Nanjing. It has branches in Nanjing, Shanghai, Pudong and Beijing.

Can we send money from China to the Philippines via these Metrobank offices?

Yes. The charge for sending money is 45 RMB. Show your tax invoice for verification, particularly for larger amounts.

Metropolitan Bank (China) Ltd.
35th Floor Lianqiang International Tower
289 Jiangdongzhong Road
Jianye District, Nanjing
Tel No:  86-25-6858-4111

Nanjing

Ground Floor Lianqiang International Mansion
No. 289 Middle Jiangdongzhong Road
Jianye District, Nanjing
Tel No.:  86-25-6858-4111

Shanghai

1152 West Yan'an Road
1st/Floor Metrobank Plaza
Shanghai 200052 PROC
Tel No.:  86-21-6191-0799, 86-21-6191-0777

Pudong

1203 Marine Tower
1 Pudong Ave.
Shanghai 200120 PROC
Tel No.:  86-21-6886-0899, 86-21-6886-0008

Beijing

14th Floor Room 1410, Office Tower One
Henderson Center, 18 Jian Guo Men Nei St.
Beijing
Tel No:  86-10-6518-3359

Yes, there's a Philippine bank in China.