Rhandsontable collect values from logical == TRUE

You could try the following approach. Use hot_to_r to get your data from the handsontable as an R object. Check the first column for any checked items (which would be TRUE boolean values). If there are, you can extract the second column of data, using the row indices based on the first column that are TRUE.

Note that the code in output$selected can be moved to a separate reactive expression, so that the selected results can be used elsewhere.

Also, you would need parentheses for selected2(). selected2() should return a character vector of the Type selected.

To select the appropriate columns from your second data.frame Aims_DF_NEW, you can try:

Aims_DF_NEW[, names(Aims_DF_NEW) %in% selected2(), drop = F]

This will only include columns in Aims_DF_NEW that are included in the selected2() result. drop = F is added so the result is not coerced to a vector if only 1 column selected (and remains a data.frame).

Here is a revised version to subset the second table based on the first table (second table simplified to demonstrate).

library(rhandsontable)
library(shiny)

orgs <- c("Community leaders/representatives",
          "Members of local community/indigenous committees",
          "Landowners/customary area owners",
          "National government",
          "Sub-national or local government",
          "Managed area manager/personnel",
          "International NGO",
          "Local or national NGO",
          "Community based organizations - women’s groups",
          "Community based organizations - men’s groups",
          "Community based organizations - youth/school groups",
          "Community based organizations - religious groups",
          "Community based organizations - conservation groups",
          "Industry", 
          "Private sector",
          "Academic institute or research facility",
          "Other")

proj_aim3 <- data.frame(Category = c("Area", "Condition", "Diversity"))
proj_aim3 <- cbind(proj_aim3, setNames( lapply(orgs, function(x) x=NA), orgs))
Aims_DF_NEW <- proj_aim3
imps2 <- c("Primary", "Secondary", "Tertiary")

ui <- fluidPage(
  rHandsontableOutput('Intiated'),
  verbatimTextOutput('selected'),
  br(),
  rHandsontableOutput("Aims2")
)

server <- function(input, output, session) {
  
  cats <- c("Community leaders/representatives", "Members of local community/indigenous committees", "Landowners/customary area owners", "National government", "Sub-national or local government", "Managed area manager/personnel",
            "International NGO", "Local or national NGO", "Community based organizations - women’s groups", "Community based organizations - men’s groups",
            "Community based organizations - youth/school groups", "Community based organizations - religious groups",  "Industry", "Private sector", 
            "Academic institute or research facility", "Not recorded", "Other")
  
  DF <- data.frame(Tick = rep(FALSE, length(cats)), Type = cats, Name = rep("", length(cats)))
  
  output$Intiated <- renderRHandsontable(
    rhandsontable(DF, selectCallback = TRUE, readOnly = FALSE)
  )
  
  selected2 <- reactive({     
    dat <- hot_to_r(input$Intiated)     
    if (any(dat[[1]])) {       
      dat[which(dat[[1]]), 2]      
    }   
  })
  
  output$selected <- renderPrint({
    cat(paste(selected2(), collapse = "\n"))
  })
  
  output$Aims2 <- renderRHandsontable({
    rhandsontable(Aims_DF_NEW[, names(Aims_DF_NEW) %in% selected2(), drop = F], rowHeaders = NULL, width = 1500, height = 600) 
  })
  
}

shinyApp(ui = ui, server = server)

Putting together the answers from @Ben. Here is a solution

library(rhandsontable)
library(shiny)

orgs <- c("Community leaders/representatives",
          "Members of local community/indigenous committees",
          "Landowners/customary area owners",
          "National government",
          "Sub-national or local government",
          "Managed area manager/personnel",
          "International NGO",
          "Local or national NGO",
          "Community based organizations - women’s groups",
          "Community based organizations - men’s groups",
          "Community based organizations - youth/school groups",
          "Community based organizations - religious groups",
          "Community based organizations - conservation groups",
          "Industry", 
          "Private sector",
          "Academic institute or research facility",
          "Other")

proj_aim3 <- data.frame(Category = c("Area", "Condition", "Diversity"))
proj_aim3 <- cbind(proj_aim3, setNames( lapply(orgs, function(x) x=NA), orgs) )

ui <- fluidPage(
  rHandsontableOutput('Intiated'),
  verbatimTextOutput('selected'),
  br(),
  rHandsontableOutput("Aims2")
)

server <- function(input, output, session) {
  
  cats <- c("Community leaders/representatives", "Members of local community/indigenous committees", "Landowners/customary area owners", "National government", "Sub-national or local government", "Managed area manager/personnel",
            "International NGO", "Local or national NGO", "Community based organizations - women’s groups", "Community based organizations - men’s groups",
            "Community based organizations - youth/school groups", "Community based organizations - religious groups",  "Industry", "Private sector", 
            "Academic institute or research facility", "Not recorded", "Other")
  
  DF <- data.frame(Tick = rep(FALSE, length(cats)), Type = cats, Name = rep("", length(cats)))
  
  output$Intiated <- renderRHandsontable(
    rhandsontable(DF, selectCallback = TRUE, readOnly = FALSE)
  )
  
  selected2 <- reactive({     
    dat <- hot_to_r(input$Intiated)     
    if (any(dat[[1]])) {       
      dat[which(dat[[1]]), 2]      
    }   
  })
  
  output$selected <- renderPrint({
    cat(paste(selected2(), collapse = "\n"))
  })
  
  
  Aims_DF_NEW <- proj_aim3
  imps2 <- c("Primary", "Secondary", "Tertiary")
  
  Cat <- data.frame(Aims_DF_NEW[, 1])
  colnames(Cat) <- c("Category")

  output$Aims2 <- renderRHandsontable({   rhandsontable(cbind(Cat, Aims_DF_NEW[, selected2(), drop = F]), rowHeaders = NULL, width = 1500, height = 600) %>%
      hot_col(col = "Category", readOnly = T) %>%
      hot_cols(cols = Aims_DF_NEW[,2:ncol(Aims_DF_NEW)], type = "autocomplete", source = imps2, strict = TRUE, colWidths = 200)})
  
}

shinyApp(ui = ui, server = server)