Dawn Sturgess, 44, died a week ago after she apparently handled a bottle contaminated with the nerve agent in the Wiltshire town at the end of June.
Her partner Charlie Rowley, 45, was also exposed to the substance and remains in hospital, where he is in a serious but stable condition.
The incident came after ex-Russian spy Sergei Skripal and his daughter Yulia were poisoned with the same substance in Salisbury in March, sparking widespread accusations that Russia was responsible.
Now the son of Ms Sturgess, teenager Ewan Hope, has called on US President Donald Trump to raise it with Mr Putin during their summit in Finland on Monday.
The pair are due to meet in Helsinki, where Mr Trump will travel to from Scotland after concluding his visit to the UK.
Mr Hope, 19, told the Sunday Mirror: “I don’t share Donald Trump’s politics and I’ll never be a supporter of his, but I would like him to raise mum’s case with the Russian president.
“We need to get justice for my mum.”
He added that he wanted the person or people responsible “to get what they deserve”.
Experts at Porton Down are attempting to determine whether the novichok that poisoned Ms Sturgess and Mr Rowley was from the same batch used in the attempted murder of the Skripals.
The UK has also invited experts from the Organisation for the Prohibition of Chemical Weapons to independently confirm the identity of the nerve agent.
It is not yet clear where the contaminated bottle came from, or how it came to be in Mr Rowley’s home where it was eventually found by police.
With the investigation ongoing, Mr Hope has reportedly been told that he may have to wait “weeks or even months” before he can bury his mother, with a post-mortem due on Tuesday and an inquest to be opened two days later.
Friends are planning their own memorial for her in the meantime, with police advising that their work in Amesbury is some of the “most complex and difficult” any force in the country has ever faced.
More than 400 exhibits, samples and items have been recovered by officers so far and searches could last months.
On Saturday, the army was seen removing an ambulance that was used in the treatment of Ms Sturgess and Mr Rowley when they first fell ill on 30 June – and officers have been looking for other possible sites or sources of contamination.
Assistant commissioner Neil Basu, national lead for counter-terrorism policing in the UK, described the process as “painstaking and vital work”.
“It is not an exaggeration to say that the search process linked with both this and the Salisbury investigation has been one of the most complex and difficult that UK policing has ever faced,” he said.
“Not only are we trying to solve an extremely serious crime that has been committed, but we’re also working to identify any potential outstanding risks to the public; all whilst ensuring that all those involved in the search process are not themselves exposed to any risk of contamination.
“It is painstaking and vital work, which unfortunately takes a very long time to complete, but I am sure that the public understands why it is absolutely necessary.”