The phrase 'for some time afterwards' is correct and usable in written English.
It can be used to refer to a period of time that follows an event or situation, such as a period of time after an occurrence or change. For example, "The business was closed for two weeks, and there were difficulties for some time afterwards as the company tried to get back on its feet."
For some time afterwards my children talked accusingly about "that nice lady you scared away".
For some time afterwards, Waugh referred to Heygate as "the basement boy".
But, then, and for some time afterwards, the process involved an extreme physical trial on the subject's part.
The derelict finally commits suicide but his memory stays with the counterman and the customer for some time afterwards.
Not only is 14 July France's most colourful national holiday – celebrated with parades, outdoor entertainment and a great many fireworks – but the party continues for some time afterwards.
During the transition, and probably for some time afterwards, shops will have to display two prices, one in euros and one in local currency.
Whether they ought to be eligible to any offices whatever during the period for which they shall be elected to serve, and even for some time afterwards--and 2. How far they ought to participate in the power of appointments.
Deila was locked in the dressing room for some time after the game, but afterwards refused to blame his players and instead took full responsibility, insisting a different line-up would not have changed the result.
The royalists were defeated, but continued to raid villages for some more time afterwards.
That helped, it helped a little, but only for some time, because afterwards I had no control … The pain was very intense, I could not control it, the breathing everybody was telling me to do to alleviate pain, I could not do it, the pain was intense".
I thought of the characters and the world I had created for them for a long time afterwards.
