Q:

How to get internet from WiFi and share to LAN router

I have a Cisco 877 Router (plus a 16 port Switch) managing my Office LAN where 10+ PCs and Network printers are connected.  I need a LAN because I run an Apache server with some web apps (accessed  only locally).  
Unfortunately, I don't have any DSL connection available.  The only access to the Internet is from a WiFi router placed in another floor of the building. 
I also have a TP-Link TL-WA830RE Range Repeater and a D-Link DWL-2200AP Wifi Access Point. 
Is it possible to get Internet access from WiFi and then share it to all PCs through the LAN? 

A:

The networking concept you're looking for is a bridge; a bridge connects two communications networks into one network.  
You should be able to configure your D-Link access point as a wireless bridge.  According to the D-Link support page, your access point should be able to run in "PtP Bridge" mode, which does exactly that.  I quote:

This selection allows the DWL-2200AP to connect to another wireless
  Access Point capable of bridging.  However, be aware that most
  manufacturers use proprietary settings when enabling bridging mode in
  the Access Point.  A typical scenario for this selection is connecting
  two buildings through a wireless connection.  Enter the MAC address of
  the remote bridge to which the AP will associate. 

An alternative is to install DD WRT and you can follow this setup guide.  Although in your case, the D-Link should be able to do this without custom firmware. 
Your networking topology should look like this:

The external access point is wirelessly connected to your D-Link access point, providing internet access. 
Your D-Link access point provides this access via a regular LAN port (the WAN port will be kept unused).  You should connect the D-Link LAN port to your switch.  Make sure your D-Link LAN ip address has an ip address in your subnet (either by static configuration or by DHCP server).