How to start a systemd service after completion of another systemd service of type "simple"

I have seen similar questions but none of them address the situation I am facing. My service A is defined as follows (Note Type=simple).

[Unit]
Description=Sample service A
Before=shutdown.target
After=multi-user.target
Requires=multi-user.target
Conflicts=shutdown.target

[Service]
Type=simple
RemainAfterExit=yes
Restart=no
ExecStart=/etc/rc.d/init.d/script_a start
ExecStop=/etc/rc.d/init.d/script_a stop

[Install]
RequiredBy=random.target

Another service B needs to be run only after the service A has run to completion. I tried the following but it seems the service B is started as soon as service A has started. Service B is not waiting for A to finish.

[Unit]
Description=Sample service B
After=serviceA.service
Requires=serviceA.service

[Service]
Type=oneshot
RemainAfterExit=yes
ExecStart=/etc/init.d/scriptb start

[Install]
RequiredBy=random.target

How can I make service B wait till A has finished?

EDIT

I also tried putting OnSuccess=serviceB.service in Service A but did not help.

In order to make service B wait until service A has finished, you can add the WantedBy option to service A and the RequiredBy option to service B, with the same target. Here's how you can modify your unit files:

For service A:

Description=Sample service A
Before=shutdown.target
After=multi-user.target
Requires=multi-user.target
Conflicts=shutdown.target

[Service]
Type=simple
RemainAfterExit=yes
Restart=no
ExecStart=/etc/rc.d/init.d/script_a start
ExecStop=/etc/rc.d/init.d/script_a stop

WantedBy=service-b.target

[Install]
RequiredBy=random.target 

For Service B:

Description=Sample service B
After=serviceA.service
Requires=serviceA.service

RequiredBy=service-b.target

[Service]
Type=oneshot
RemainAfterExit=yes
ExecStart=/etc/init.d/scriptb start

[Install]
RequiredBy=service-b.target

Service A is marked as WantedBy this target and Service B is marked as RequiredBy this target. This means that Service B will only start when the service-b.target is reached, and the service-b.target is only reached when Service A has completed successfully.