Like this:
#region WNetUseConnection
[DllImport("Mpr.dll", EntryPoint = "WNetUseConnection", CallingConvention = CallingConvention.Winapi)]
private static extern int WNetUseConnection(IntPtr hwndOwner, NETRESOURCE lpNetResource, string lpPassword, string lpUserID, int dwFlags, string lpAccessName, string lpBufferSize, string lpResult);
[DllImport("Mpr.dll", EntryPoint = "WNetCancelConnection2", CallingConvention = CallingConvention.Winapi)]
private static extern int WNetCancelConnection2(string lpName, int dwFlags, bool fForce);
[StructLayout(LayoutKind.Sequential)]
private class NETRESOURCE
{
    public ResourceScope dwScope = 0;
    public ResourceType dwType = 0;
    public ResourceDisplayType dwDisplayType = 0;
    public ResourceUsage dwUsage = 0;
    public string lpLocalName = null;
    public string lpRemoteName = null;
    public string lpComment = null;
    public string lpProvider = null;
};
public enum ResourceScope
{
    RESOURCE_CONNECTED = 1,
    RESOURCE_GLOBALNET,
    RESOURCE_REMEMBERED,
    RESOURCE_RECENT,
    RESOURCE_CONTEXT
};
public enum ResourceType
{
    RESOURCETYPE_ANY,
    RESOURCETYPE_DISK,
    RESOURCETYPE_PRINT,
    RESOURCETYPE_RESERVED
};
public enum ResourceUsage
{
    RESOURCEUSAGE_CONNECTABLE = 0x00000001,
    RESOURCEUSAGE_CONTAINER = 0x00000002,
    RESOURCEUSAGE_NOLOCALDEVICE = 0x00000004,
    RESOURCEUSAGE_SIBLING = 0x00000008,
    RESOURCEUSAGE_ATTACHED = 0x00000010,
    RESOURCEUSAGE_ALL = (RESOURCEUSAGE_CONNECTABLE | RESOURCEUSAGE_CONTAINER | RESOURCEUSAGE_ATTACHED),
};
public enum ResourceDisplayType
{
    RESOURCEDISPLAYTYPE_GENERIC,
    RESOURCEDISPLAYTYPE_DOMAIN,
    RESOURCEDISPLAYTYPE_SERVER,
    RESOURCEDISPLAYTYPE_SHARE,
    RESOURCEDISPLAYTYPE_FILE,
    RESOURCEDISPLAYTYPE_GROUP,
    RESOURCEDISPLAYTYPE_NETWORK,
    RESOURCEDISPLAYTYPE_ROOT,
    RESOURCEDISPLAYTYPE_SHAREADMIN,
    RESOURCEDISPLAYTYPE_DIRECTORY,
    RESOURCEDISPLAYTYPE_TREE,
    RESOURCEDISPLAYTYPE_NDSCONTAINER
};
#endregion WNetUseConnection
And here is how to use it:
(It is enough if you do this once, you don't have to repeat it before every access to the share.)
// Initialize connection to file share
NETRESOURCE nr = new NETRESOURCE();
nr.dwType = ResourceType.RESOURCETYPE_DISK;
nr.lpRemoteName = "\\192.168.1.1";
string user = "user B";
string password = "password for user B";
WNetUseConnection(IntPtr.Zero, nr, password, user, 0, null, null, null);