The phrase 'strengthen through' is correct and usable in written English.
You can use it when referring to making something stronger or more efficient. For example, "The team worked to strengthen their relationship through openness and communication."
The storm was expected to strengthen through Tuesday and begin moving east on Wednesday, possibly lasting until Friday, she said.
"We expect household consumption to strengthen through the second half of this year, as a number of government schemes designed to promote lending, even to the riskiest of prospects, start to bear fruit".
She added: "We certainly need companies investing more and creating a bigger footprint in fast-growing markets, and while some risks remain, we expect the economy to continue to strengthen through 2014".
The relationships start off weak – a retweet, @ reply, or blog comment – but often strengthen through further discussions and eventually become new friendships and business relationships".
It is currently "hurtling along" on the back of a strong jet stream and is expected to deepen and strengthen through Sunday as it approaches the UK, he says.
The values upon which this organization is based not only remain intact, but continue to strengthen through dialogues with the scientific community and through actions that advance science for the benefit of all.
So overall I can report a British economy strengthening through 2004.
Access to agricultural extension (advisory) services is weak and its nutrition policies need strengthening through, for example, time-bound nutrition targets.
Stocks strengthened through the day.
It strengthened through 2008 but weakened in 2009.
The court has been strengthened through the new charter of fundamental rights.
