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I am writing a letter to a client and am at odds with my boss over this. Could you please advise? Here is the part of the letter in question:
"Please be advised that we recently conducted a telephone conference with the plaintiff’s attorney in the above-captioned matter. At this time, we requested information and/or documentation pertaining to both plaintiffs’ medical conditions and lost wages claims." The question that I have is in regard to the phrase "at this time." I think it is correct while the boss says it should be "at that time." I think it can go either way as "at that time" demonstrates keeping the subject of the letter in the past while "at this time" demonstrates a time sequence in the letter. Please help!
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Try a search at

with:
site:bbc.co.uk "at this time"
and separately with:
site:bbc.co.uk "at that time"
(quotation marks are important)
which will perform a search on that bastion of good English, the BBCEmotion: smile

You will find that "at that time" is related mostly with past tense, while "at this time" is mostly related to present tense (you're free to perform some stats and confront me on that, but ...). Thus your boss is, in general, correct.

However, you will find examples where the time is "localized" to the general time of the sentence, and "at this time" will be used for describing events which took place a long time ago:
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BBC - North East Wales Denbighshire history - Memories of ...

In 1954, as a 16 year old, I took up motorcycling and often visited Sun Garage motorcycle showroom and workshop and petrol outlet located on Regent Street opposite the junction with Church Street. These were exciting times for it was an opportunity to view the new machines in the showroom and chance to talk to Alan, Les, and Horace who I believe were partners in the business. It is amazing now to think that at this time petrol was dispensed from attended pumps located at the busy roadside. On one occasion sitting astride my BSA bantam motorcycle, Horace, a heavy smoker, served me with fuel. I recall I was horrified and too frightened to move or say anything, for Horace dispensed the fuel with a lighted cigarette dangling from his lips. I never ever went back there for fuel again.

http://www.bbc.co.uk/wales/northeast/sites/denbighshire/pages/int-eist1.shtml
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Thus time is relative, and an author can focus on the local time of the sentence and prefer/pretend to say "at this time," but see the preferences in the above.

This being a business letter, be conventional, as you want to minimize confusion.

N.B. Should you prefer AmE to BrE, make searches at the New York Times, with:

site:nytimes.com "at this time"

where the first hit gives something similar to your preference:
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But beginning in 2002, the United States branded North Korea as part of an axis of evil, threatened military action, ended the shipments of fuel oil and the construction of nuclear power plants and refused to consider further bilateral talks. In their discussions with me at this time, North Korean spokesmen seemed convinced that the American positions posed a serious danger to their country and to its political regime.

Jimmy Carter, in the New York Times
http://tinyurl.com/gv2kq
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Because of the nature of this question is related to the legal aspect, words are critically important. Base on the context,

I am inclined to say [at that time] is more logical.

"Please be advised that we recently conducted a telephone conference with the plaintiff’s attorney in the above-captioned matter. At this time, we requested information and/or documentation pertaining to both plaintiffs’ medical conditions and lost wages claims."

First, we must agree that the time frame in which the conference was conducted was sometime in the past. As this is true, [at that time] we requested information and/or documentation pertaining to both plaintiffs’ medical conditions and lost wages claims” then will refer to a statement made after the conference. So [at that time] is correct.

Let’s say the same conference /deposition is scheduled for next week and you are making the same request, then [at this time] would be appropriate. Because [at this time] implies [now] and you are making the request as you speak.

"At this time, may I have everyone’s attention for a minute." – as the M.C. makes a speech for a wedding ceremony.

I was 20 years old when I had to drop out of college for a year because at that time, my parent could not afford to pay for my tuition. - [at that time] is correct.

Rule of thumb:

At that time – time passed.

At this time - as you speak
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Could we widen the scope of possibilities to include at the same time and at the time?

I mention this because both of the original options seem to allow a alternative reading which implies that there were others moments in time when the same action was not performed, even though it could/should have been done.
Good point! I don’t see why not!Emotion: smile
Hi guys,

I'd like to offer an additional approach for you to consider in this excellent discussion.

In spatial terms, 'this' and 'that' relate to the concept of 'near' and 'far', eg this book vs. that book.

I have some of the same feeling about at this time and at that time.

At this time suggests to me some personal involvement, 'some closeness', by the speaker. eg 'At this time, he confessed to me that he robbed the bank'.

At that time does not so strongly suggest to me personal involvement by the speaker. eg 'At that time, he confessed to the police officer that he robbed the bank'.

It's just a subtle difference, not a clear and absolute rule.

Best wishes, Clive
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Well, yes, that can bring some detachment/rationality to the text, while this makes it more personal, you're getting in there yourself.