Go to current directory when you open screen or a new tab in screen.

.screen.sh

#!/bin/bash
# The file where the PWD is going to be shared with other (new) tabs.
STY_SHARED_PWD="/tmp/.screenpwd-$STY"
if [ -e "$STY_SHARED_PWD" ] ; then
    # If the file exists, then another session had already set the
    # environment, so read the most recent PWD and go to the directory.
    STY_PWD="$(</tmp/.screenpwd-$STY)"
    # Provided that it's not empty.
    [ -n "$STY_PWD" ] && cd "$STY_PWD"
fi
# Always write the latest location to the shared file.
export PROMPT_COMMAND="echo -n \"\$PWD\" > \"$STY_SHARED_PWD\""

# Start the real shell
export SHELL=bash
bash "$@"

# When the screen exits, remove the temporary file.
[[ -e "$STY_SHARED_PWD" ]] && rm "$STY_SHARED_PWD"

.screenrc

# Wrapped shell to ensure that PWD is always the latest PWD
shell $HOME/.screen.sh