Raspberry Pi: AP + client mode

commands.sh

#!/bin/sh
# The script configures simultaneous AP and Managed Mode Wifi on Raspberry Pi Zero W (should also work on Raspberry Pi 3)
# Usage: curl https://gist.githubusercontent.com/aceisace/b7ca22b50531f43d48c74d86eb62c89a/raw | sh -s WifiSSID WifiPass APSSID APPass
# Licence: GPLv3
# Author: Darko Lukic <lukicdarkoo@gmail.com>
# Special thanks to: https://albeec13.github.io/2017/09/26/raspberry-pi-zero-w-simultaneous-ap-and-managed-mode-wifi/

MAC_ADDRESS="$(cat /sys/class/net/wlan0/address)"
CLIENT_SSID="${1}"
CLIENT_PASSPHRASE="${2}"
AP_SSID="${3}"
AP_PASSPHRASE="${4}"

# Install dependencies
sudo apt -y update
sudo apt -y upgrade
sudo apt -y install dnsmasq dhcpcd hostapd

# Populate `/etc/udev/rules.d/70-persistent-net.rules`
sudo bash -c 'cat > /etc/udev/rules.d/70-persistent-net.rules' << EOF
SUBSYSTEM=="ieee80211", ACTION=="add|change", ATTR{macaddress}=="${MAC_ADDRESS}", KERNEL=="phy0", \
  RUN+="/sbin/iw phy phy0 interface add ap0 type __ap", \
  RUN+="/bin/ip link set ap0 address ${MAC_ADDRESS}
EOF

# Populate `/etc/dnsmasq.conf`
sudo bash -c 'cat > /etc/dnsmasq.conf' << EOF
interface=lo,ap0
no-dhcp-interface=lo,wlan0
bind-interfaces
server=8.8.8.8
domain-needed
bogus-priv
dhcp-range=192.168.4.2,192.168.4.20,24h
EOF

# Populate `/etc/hostapd/hostapd.conf`
sudo bash -c 'cat > /etc/hostapd/hostapd.conf' << EOF
ctrl_interface=/var/run/hostapd
ctrl_interface_group=0
interface=ap0
ssid=${AP_SSID}
hw_mode=g
channel=1
wmm_enabled=0
macaddr_acl=0
auth_algs=1
ignore_broadcast_ssid=0
wpa=2
wpa_passphrase=${AP_PASSPHRASE}
wpa_key_mgmt=WPA-PSK
wpa_pairwise=TKIP
rsn_pairwise=CCMP
EOF

# Populate `/etc/default/hostapd`
sudo bash -c 'cat > /etc/default/hostapd' << EOF
DAEMON_CONF="/etc/hostapd/hostapd.conf"
EOF

# Populate `/etc/wpa_supplicant/wpa_supplicant.conf`
sudo bash -c 'cat > /etc/wpa_supplicant/wpa_supplicant.conf' << EOF
country=DE
ctrl_interface=DIR=/var/run/wpa_supplicant GROUP=netdev
update_config=1

network={
    ssid="${CLIENT_SSID}"
    psk="${CLIENT_PASSPHRASE}"
    id_str="AP1"
}
EOF

# Populate `/etc/network/interfaces`
sudo bash -c 'cat > /etc/network/interfaces' << EOF
source-directory /etc/network/interfaces.d

auto lo
auto ap0
auto wlan0
iface lo inet loopback

allow-hotplug ap0
iface ap0 inet static
    address 192.168.4.1
    netmask 255.255.255.0
    hostapd /etc/hostapd/hostapd.conf

allow-hotplug wlan0
iface wlan0 inet manual
    wpa-roam /etc/wpa_supplicant/wpa_supplicant.conf
iface AP1 inet dhcp
EOF

# Populate `/bin/start_wifi.sh`
sudo bash -c 'cat > /bin/start_wifi.sh' << EOF
echo 'Starting Wifi AP and client...'
sleep 30
sudo ifdown --force wlan0
sudo ifdown --force ap0
sudo ifup ap0
sudo ifup wlan0
sudo sysctl -w net.ipv4.ip_forward=1
sudo iptables -t nat -A POSTROUTING -s 192.168.4.0/24 ! -d 192.168.4.0/24 -j MASQUERADE
sudo systemctl restart dnsmasq
EOF
sudo chmod +x /bin/start_wifi.sh
crontab -l | { cat; echo "@reboot /bin/start_wifi.sh"; } | crontab -
echo "Wifi configuration is finished! Please reboot your Raspberry Pi to apply changes..."

Wonderful script from Darko Lukic, modified slightly to my needs.
Just a side note, it seems (through) trial and error at least, that the channel of the router must match the channel of the AP.